Time and Distance

Aditya's speed is 20 km/hr, which can be converted to m/sec by multiplying it by 5/18. 

This results in a speed of 50/9 m/sec. To cover a distance of 400 m at this speed, 

it will take Aditya 72 seconds, or 1 1/5 minutes. 

This can also be expressed as 1 12/60 minutes.

The speed of the cyclist is 18 km/hr. 

This was calculated by dividing the distance traveled, 750 m, by the time taken, 2 minutes and 30 seconds, which is equal to 150 seconds. 

The speed in meters per second is then calculated by dividing the distance traveled by the time taken, resulting in a speed of 5 m/sec. 

This speed can then be converted to km/hr by multiplying it by 18/5.

To compare the speeds of the dog and hare, we need to express their respective speeds in the same units, such as feet per second. 

Since the dog takes 4 leaps for every 5 leaps of the hare, and each leap of the dog is equal to 3 leaps of the hare, the ratio of the lengths of the leaps of the dog to the hare is 3:4.

If we let "d" represent the speed of the dog and "h" represent the speed of the hare, we can set up the following proportion:

4d = 5h

3h = 4d

To solve this proportion, we can cross-multiply:

(4d)(4) = (5h)(3)

16d = 15h

d/h = 15/16

This means that the speed of the dog is 15/16 of the speed of the hare. 

In other words, the hare is slightly faster than the 

dog.

Since the distance is given in kilometers and the time is 

given in hours, you can set up the following proportion to 

solve for the speed in kilometers per hour:

(distance covered)/(time taken) = speed

(5/3 speed)/(1 2/3 hours) = speed

To solve this proportion, you can cross-multiply:

(5/3 speed)(1 2/3 hours) = speed

5/3 speed = 2/3 speed

5/3 = 2/3

Multiplying both sides by 3/5 gives us:

1 = 2/5

Multiplying both sides by 5/2 gives us:

5/2 = 2

Therefore, the speed is 5/2 kilometers per hour, or 5/3 meters 

per second.

The average speed of the vehicle is calculated by dividing the distance traveled by the time taken. 

The distance traveled is given as 2xy km, and the time taken is given as x+y hours.

Therefore, the average speed is 2xy km / (x+y) hours.

The distance traveled in 5 hours and 48 minutes is calculated by multiplying the average speed by the time taken. 

The average speed is given as 200/29 km/hr and the time taken is given as 5 hours and 48 minutes, 

which is equivalent to 29/5 hours. 

Therefore, the distance traveled is (200/29 km/hr) * (29/5 hours) = 40 km.

The distance of the post office from the village is calculated by dividing the distance traveled by 2, 

since the vehicle traveled to the post office and back. 

In this case, the distance traveled was 40 km, 

so the distance of the post office from the village is 40 km / 2 = 20 km.

The total distance traveled around the square is given as the sum of the distances traveled along each side. 

Since each side of the square is x km long and there are four sides, the total distance traveled is 4x km.

The total time taken to fly around the square is given as the sum of the times taken to fly along each side. 

Since the speed of the plane along each side is given, we can divide the distance traveled by the speed to find the time taken for each side. 

For example, to find the time taken to fly 200 km at a speed of 200 km/hr, we would divide 200 km by 200 km/hr to get 1 hour. 

Therefore, the total time taken to fly around the square is x/200 + x/400 + x/600 + x/800 hours.

To find the average speed, we can divide the total distance traveled by the total time taken. In this case, the total distance traveled is 4x km and the total time taken is x/200 + x/400 + x/600 + x/800 hours. 

Therefore, the average speed is 4x km / (x/200 + x/400 + x/600 + x/800) km/hr.

By substituting the values given in the problem, we can solve for y, which is the average speed. 

In this case, the average speed is y = (4x km) / (x/200 + x/400 + x/600 + x/800) km/hr. 

Plugging in the values given in the problem, 

we get y = (4x km) / ((x/200) + (x/400) + (x/600) + (x/800)) km/hr 

= (4x km) / (25x/2500) km/hr = (4x km) / (4x/y) km/hr = 

y = 2400*4/25 

= 384 km/hr.

The new speed of the vehicle is given as 5/6 of the usual speed. This means that the vehicle is traveling at a speed that is 5/6 of its normal speed.

The new time taken to travel a certain distance is given as 6/5 of the usual time. This means that it takes the vehicle 6/5 of the time it would normally take to travel the same distance.

The difference between the new time taken and the usual time taken is given as 10 minutes. This means that the new time taken is 10 minutes longer than the usual time taken.

The difference in the time taken to travel a certain distance at two different speeds is given as 1 minute, or 1/2 hour.

The time taken to travel the distance at the slower speed is given as 1/5 of the time taken to travel the same distance at the faster speed.

We can set up an equation to represent the relationship between the time taken at the two speeds and the distance traveled. 

In this case, the equation is (distance traveled at slower speed) / (time taken at slower speed) - (distance traveled at faster speed) / (time taken at faster speed) = difference in time taken.

We can solve for the distance traveled by rearranging the equation to isolate the distance traveled. 

The equation given is 

(distance traveled at slower speed) / (1/5 of the time taken at faster speed) - (distance traveled at faster speed) / (time taken at faster speed) = 1/2 hour. 

We can rewrite this as (distance traveled at slower speed) / (1/5 of the time taken at faster speed) = (distance traveled at faster speed) / (time taken at faster speed) + 1/2 hour. 

Then, we can solve for the distance traveled by multiplying both sides of the equation by 5/6. This gives us (5/6 of the distance traveled at slower speed) = (5/6 of the distance traveled at faster speed) + 5/12 hour. 

Finally, we can solve for the distance traveled by subtracting (5/6 of the distance traveled at faster speed) from both sides of the equation, which gives us (5/6 of the distance traveled at slower speed) - (5/6 of the distance traveled at faster speed) = 5/12 hour. 

This simplifies to (1/6 of the distance traveled) = 5/12 hour, or x/6 = 5/12 hour. 

Solving for x gives us x = 6 km.

The time at which the two vehicles meet is given as x hours after 10 a.m.

The distance traveled by the first vehicle in x hours is given as 65x km, and the distance traveled by the second vehicle in x-1 hours is given as 35(x-1) km.

The total distance traveled by both vehicles is given as 390 km.

We can set up an equation to represent the relationship between the distance traveled by each vehicle and the time at which they meet. In this case, the equation is (distance traveled by first vehicle in x hours) + (distance traveled by second vehicle in x-1 hours) = total distance traveled.

We can solve for the time at which the vehicles meet by rearranging the equation to isolate the time. 

The equation given is (distance traveled by first vehicle in x hours) + (distance traveled by second vehicle in x-1 hours) = total distance traveled. 

We can solve for x by subtracting (distance traveled by second vehicle in x-1 hours) from both sides of the equation, 

which gives us (distance traveled by first vehicle in x hours) - (distance traveled by second vehicle in x-1 hours) = total distance traveled - (distance traveled by second vehicle in x-1 hours). 

This simplifies to (65x - 35(x-1)) = 390 - 35(x-1). Solving for x gives us x = 17/4.

Since x is the time at which the vehicles meet, given in hours, 

the time at which they meet is 17/4 hours after 10 a.m., or 2.15 p.m.

The speed of the goods train is given as x kmph.

The distance traveled by the goods train in 10 hours is given as 10x km.

The distance traveled by an express train in 4 hours is given as 90 km.

We can set up an equation to represent the relationship between the distance traveled by each train and the time taken to travel that distance. In this case, 

the equation is (distance traveled by goods train in 10 hours) = (distance traveled by express train in 4 hours).

We can solve for the speed of the goods train by rearranging the equation to isolate the speed. 

The equation given is (distance traveled by goods train in 10 hours) = (distance traveled by express train in 4 hours). 

We can solve for x by dividing both sides of the equation by 10 and 4, respectively, 

which gives us (x kmph) = (90 km / 4 hours). 

Solving for x gives us x = 36 kmph.

The relative speed of the policeman and the thief is given as the speed of the policeman minus the speed of the thief, or 2 km/hr.

The distance between the thief and the policeman is given as 100 meters.

We can use the relative speed to calculate the time it will take for the policeman to catch up to the thief. Since the relative speed is 2 km/hr and the distance between the thief and the policeman is 100 meters, 

the time it will take for the policeman to catch up to the thief is 

100 meters / (2 km/hr * 1000 meters/km) = 1/20 hr.

To find the distance the thief will have run in 1/20 hr at a speed of 8 km/hr, we can use the formula for distance traveled, which is distance = speed * time. 

Plugging in the values given in the problem, we get distance = 8 km/hr * 1/20 hr = 2/5 km = 400 meters.

Therefore, the thief will have run a distance of 400 meters before being overtaken by the policeman.

The distance traveled by the person is given as x km.

The total time taken to walk x km and ride x km is given as 37 minutes.

The total time taken to walk 2x km and ride 2x km is given as 74 minutes.

The time taken to walk 2x km is given as 55 minutes.

We can use the given information to find the time taken to ride 2x km. 

Since the total time taken to walk 2x km and ride 2x km is 74 minutes and the time taken to walk 2x km is 55 minutes, 

the time taken to ride 2x km is 74 minutes - 55 minutes = 19 minutes.

The distance from A to B is given as d km.

The average speed is calculated using the formula average speed = total distance traveled / total time taken.

The total distance traveled is given as 2d km, which is the distance from A to B plus the distance from B to A.

The total time taken is calculated by adding the time taken to travel from A to B to the time taken to travel from B to A. 

The time taken to travel from A to B is given as d/20 hours, and the time taken to travel from B to A is given as d/30 hours.

Plugging the values for total distance traveled and total time taken into the formula for average speed, 

we get average speed = (2d km) / [(d/20 hours) + (d/30 hours)].

Simplifying the expression for total time taken, we get average speed = (2d km) / [5d/60 hours].

Finally, we can solve for the average speed by dividing both sides of the equation by 5d/60 hours, 

which gives us average speed = (2d km) / (5d/60 hours) = 24 km/hr

The speed of the object is given as 12 m/s.

The time taken to travel a certain distance is given as 3 hours 45 minutes, or 3 3/4 hours, or 15/4 hours.

To find the distance traveled by the object, we can use the formula distance = speed * time. 

Plugging in the values given in the problem, we get distance = 12 m/s * 15/4 hours.

To convert the speed from meters per second to kilometers per hour, 

we can multiply it by the conversion factor 18/5. This gives us a speed of 12 * 18/5 = 21.6 km/hr.

Plugging the converted speed into the formula for distance, we get distance = 21.6 km/hr * 15/4 hours = 162 km.

The distance traveled by another person in a certain amount of time is given as 1.6 km.

The time taken by Amar to travel the same distance is given as 18/4.8 hours.

We can use the given information to find the distance traveled by Amar by dividing the distance traveled by the other person by the time taken by Amar. 

In this case, the distance traveled by Amar is given as (distance traveled by other person) / (time taken by Amar) = 1.6 km / (18/4.8 hours).

Simplifying the expression for time taken by Amar, 

we get (distance traveled by other person) / (time taken by Amar) = 1.6 km / (3/8 hours).

Solving for the distance traveled by Amar, 

we get distance traveled by Amar 
= (distance traveled by other person) / (time taken by Amar) 

= 1.6 km / (3/8 hours) = 600 meters.



                          
                        

The time taken to reach the destination is given as 3x hours.

The distance to the destination is given as 40 * 3x = 120x km.

The person has traveled a distance of 2/3 * 120x = 80x km in 1/3 * 3x = x hours.

Therefore, to reach the destination, the person must travel the remaining distance of 40x km in 2x hours.

To find the required speed, we can use the formula speed = distance / time. 

Plugging in the values given in the problem, we get speed = 40x km / 2x hours = 20 km/hr.

The speed of the object is given as 72 km/hr.

To convert the speed from kilometers per hour to meters per second, 

we can multiply it by the conversion factor 5/18. 

This gives us a speed of 72 * 5/18 = 20 m/s.

The time taken to travel a certain distance is given as 30 seconds.

To find the distance traveled by the object, we can use the formula distance = speed * time. 

Plugging in the values given in the problem, 

we get distance = 20 m/s * 30 seconds 

= 600 meters.

The speed ratio between the two objects is given as 1:4/5 = 5:4.

The time ratio between the two objects is given as 4:5.

We can use the speed ratio and the time ratio to find the unknown time ratio. 

Since the speed ratio is 5:4 and the time ratio is 4:5, we can set up the following equation: 5/4 = (time ratio)/5.

Solving for the time ratio, we get time ratio = 5 * (5/4) = 5 * 1.25 = 20.

Therefore, the time ratio between the two objects is 20.

The total distance traveled by the person is given as 3 km.

The distance traveled by the person in a particular direction (west) is given as 1 km.

To find the distance traveled by the person in the other direction (north), 

we can subtract the distance traveled in the west direction from the total distance traveled. 

In this case, the distance traveled in the north direction is 3 km - 1 km = 2 km.

The speed ratio between the two objects is given as 1:7/6 = 6:7.

The time ratio between the two objects is given as 7:6.

We can use the speed ratio and the time ratio to find the unknown time ratio. 

Since the speed ratio is 6:7 and the time ratio is 7:6, 

we can set up the following equation: 6/7 = (time ratio)/4.

Solving for the time ratio, we get time ratio 

= 4 * (6/7) = 4 * 0.85714 

= 3.42857.

To express the time ratio in minutes, we can multiply it by 60, which gives us 3.42857 * 60 = 205.714 minutes, or approximately 28 minutes.

Therefore, the time ratio between the two objects is approximately 28 minutes.

The person traveled a distance of 6 km at a speed of 1.5 km/hr. The time taken for this leg of the journey is given as 6 km / 1.5 km/hr = 4 hours.

The person traveled a distance of 8 km at a speed of 2 km/hr. The time taken for this leg of the journey is given as 8 km / 2 km/hr = 4 hours.

The person traveled a distance of 32 km at a speed of 8 km/hr. The time taken for this leg of the journey is given as 32 km / 8 km/hr = 4 hours.

The total distance traveled by the person is given as the sum of the distances traveled in each leg of the journey, which is 6 km + 8 km + 32 km = 46 km.

The total time taken by the person is given as the sum of the times taken for each leg of the journey, which is 4 hours + 4 hours + 4 hours = 12 hours.

To find the average speed of the person, we can use the formula average speed = total distance / total time. Plugging in the values given in the problem, we get average speed = 46 km / 12 hours = 3 (5/6) km/hr.

The distance between the two locations is given as x.

The time difference between the arrival of the two cars is given as 4 hours.

We are given that the second car starts 1.5 hours later and reaches 2.5 hours earlier than the first car.

We can use the time difference and the information about the arrival times of the two cars to find the speed of the first car and the speed of the second car. Since the second car starts 1.5 hours later and reaches 2.5 hours earlier, the time taken by the second car is 4 hours - 1.5 hours - 2.5 hours = 0.5 hours. Thus, the speed of the second car is x/0.5 = 2x/1 = 2x km/hr.

The time taken by the first car is 4 hours. Thus, the speed of the first car is x/4 = x/4 km/hr.

We can use the speed of the first car and the speed of the second car to find the distance between the two locations. Since the speed of the first car is x/4 km/hr and the speed of the second car is 2x km/hr, we can set up the following equation: x/4 - 2x/4 = 4.

Solving for x, we get x = 240 km.

Therefore, the distance between the two locations is 240 km.

The distance between the two locations is given as x km.

We are given that the time difference between the arrival of the two cars is 1/2 hour.

The speed of the first car is given as 3 km/hr and the speed of the second car is given as 4 km/hr.

We can use the time difference and the speeds of the two cars to find the distance between the two locations. 

Since the time difference is 1/2 hour and the speed of the first car is 3 km/hr and the speed of the second car is 4 km/hr, 

we can set up the following equation: 

(3 km/hr - 4 km/hr)/(1/2 hr) = 1/2.

Solving for x, we get x = 6 km.

Therefore, the distance between the two locations is 6 km.

The speed of the first train is given as x and the speed of the second train is given as y.

The length of the first train is given as 27x and the length of the second train is given as 17y.

The relative speed of the two trains is given as x + y.

The time taken for the two trains to cross each other is given as 23 seconds.

We can use the lengths of the trains, the relative speed, and the time taken for the trains to cross each other to find the speed ratio between the two trains. Since the time taken for the trains to cross each other is 23 seconds and the relative speed is x + y, we can set up the following equation: (27x + 17y)/(x + y) = 23.

Solving for x, we get x = (6y)/4.

The speed ratio between the two trains is given by the ratio of their speeds, which is x/y. Plugging in the value of x that we found in step 6, we get x/y = (6y)/(4y) = 3/2.

Therefore, the speed ratio between the two trains is 3/2.

The distance traveled by the object is given as 150 meters.

The speed of the object is given as 54 km/hr.

We can use the formula time = distance/speed to find the time taken for the object to travel the given distance. Plugging in the values given in the problem, we get time = 150 meters / (54 km/hr * 5/18).

Solving for time, we get time = 10 seconds.

Therefore, the time taken for the object to travel the given distance is 10 seconds.

The speed of the first train is given as 50 km/h and the speed of the second train is given as 400/7 km/h.

The time at which the two trains will meet is given as x hours after 6:00 a.m.

The distance between the starting points of the two trains is given as 200 km.

We can use the speeds of the trains, the time at which they will meet, and the distance between their starting points to find the required time. Since the speed of the first train is 50 km/h and the speed of the second train is 400/7 km/h, we can set up the following equation: x * 50 + (x - 2) * 400/7 = 200.

Solving for x, we get x = 2200/750.

The required time is given as x hours after 6:00 a.m. Plugging in the value of x that we found in step 5, we get the required time as 8:56 a.m.

Therefore, the two trains will meet at 8:56 a.m.

The total distance traveled by the vehicle is given as 595 km.

The total time taken by the vehicle is given as 8.5 hours.

We can use the formula for average speed, which is total distance traveled / total time taken, to find the average speed of the vehicle. Plugging in the values given in the problem, we get average speed = 595 km / 8.5 hours.

Solving for average speed, we get average speed = 70 km/hr.

Therefore, the average speed of the vehicle is 70 km/hr

The slower speed of the train is given as V km/h.

We are given that the train takes 8 hours to travel a certain distance at the slower speed and takes 20/3 hours to travel the same distance at a faster speed.

We can use the formula V1 x t1 = V2 x t2 to find the slower speed of the train. 

Plugging in the values given in the problem, we get V x 8 = (V + 5) x 20/3.

Solving for V, we get V = 25 km/h.

Therefore, the slower speed of the train is 25 km/h.

The length of the first train is given as 125 meters and the length of the second train is given as X meters.

The speed of both trains is given as 5 m/s.

The time taken for the second train to pass a certain point is given as 60 seconds.

We can use the speed and time taken to find the length of the second train. 

Since the speed of the train is 5 m/s and the time taken is 60 seconds, 

we can set up the following equation: 

(125 + X)/5 = 60.

Solving for X, we get X = 175 meters.

Therefore, the length of the second train is 175 meters.

The speed of the object is given as 54 km/hr.

The time taken to travel a certain distance is given as 9 seconds.

We can use the formula distance = speed x time to find the distance traveled by the object. 

Plugging in the values given in the problem, we get distance 

= (54 km/hr * 5/18) x 9 seconds.

Solving for distance, we get distance = 135 meters.

Therefore, the distance traveled by the object is 135 meters.

The total distance covered by the two trains is given as 200 meters.

The time taken for the trains to pass each other is given as 8 seconds.

The speed of the slower train is given as v km/hr and the speed of the faster train is given as 2v km/hr.

The relative speed of the two trains is the sum of their individual speeds, which is given as 3v km/hr.

We can use the relative speed, total distance covered, and time taken to find the speed of the two trains. Since the relative speed is 3v km/hr and the total distance covered is 200 meters, we can set up the following equation: 3v = 200/8 m/s = 25 m/s.

Solving for v, we get v = 25/3 m/s.

The speed of the faster train is given as 2v km/hr. Plugging in the value of v that we found in step 6, we get the speed of the faster train as 2v = (50/3) * (36/10) km/hr = 5 * 36/3 = 5 * 12 = 60 km/hr.

Therefore, the speed of the slower train is 25/3 m/s and the speed of the faster train is 60 km/hr.

The distance traveled by the vehicle is given as 160 meters.

The time taken to travel that distance is given as 18 seconds.

We can use the formula speed = distance/time to find the speed of the vehicle. Plugging in the values given in the problem, we get speed = 160 meters / 18 seconds.

Solving for speed, we get speed = 8.88 m/s.

The speed of the vehicle is also given in km/hr, so we need to convert the speed from m/s to km/hr. 

We can use the formula speed (km/hr) = speed (m/s) * (18/5). 

Plugging in the value of speed that we found in step 4, we get speed = 8.88 m/s * (18/5) km/hr.

Solving for speed, we get speed = 32 km/hr.

Therefore, the speed of the vehicle is 32 km/hr.

The time taken by the man on the motorcycle to reach Bharatpur is given as 192/32 = 6 hours.

The man in the car starts from Delhi 2.5 hours after the man on the motorcycle starts. Therefore, the time taken by the man in the car to reach Bharatpur is 6 hours - 2.5 hours = 3.5 hours.

The man in the car reaches Bharatpur half an hour late, so the total time taken by him is 3.5 hours + 0.5 hours = 4 hours.

The ratio of the time taken by the man on the motorcycle to the time taken by the man in the car is 4 hours:6 hours, which simplifies to 2:3.

Therefore, the ratio of the time taken by the man on the motorcycle to the time taken by the man in the car is 2:3.

The distance between the two stations is given as x.

Train T1 takes 5 hours to reach Mumbai and train T2 takes 6 hours to reach Ahmedabad.

The relative speed of the two trains is given as the sum of their individual speeds, which is x/5 + x/6 = 11x/30.

The time taken for the trains to pass each other is given as x/11x/30 = 30/11.

The time taken for the trains to pass each other can be expressed in hours as (30/11) hours = 2.43 hours.

The time at which the trains pass each other is given as 7 a.m. + 2.43 hours = 9.43 a.m.

Therefore, the trains will pass each other at 9.43 a.m

The first car travels for 30 minutes at a speed of 40 kmph. The distance traveled in this time can be calculated using the formula distance = speed x time, which gives us distance = 40 kmph x (30 minutes / 60 minutes) = 20 km.

The car then travels for 45 minutes at a speed of 60 kmph. The distance traveled in this time can be calculated using the formula distance = speed x time, which gives us distance = 60 kmph x (45 minutes / 60 minutes) = 45 km.

The car then travels for 2 hours at a speed of 70 kmph. The distance traveled in this time can be calculated using the formula distance = speed x time, which gives us distance = 70 kmph x 2 hours = 140 km.

The total distance traveled by the car is the sum of the distances traveled in each of the three time periods, which is 20 km + 45 km + 140 km = 205 km.

The total time taken by the car is the sum of the times taken in each of the three periods, which is 30 minutes + 45 minutes + 2 hours = 3.25 hours.

The average speed of the car can be calculated using the formula average speed = total distance / total time, which gives us average speed = 205 km / 3.25 hours = 63.07 km/h.

The tiger takes 5 leaps per minute and the deer takes 4 leaps per minute.

The speed of the tiger can be calculated using the formula speed = number of leaps per minute x distance covered per leap, which gives us speed = 5 leaps/minute x 8 meters/leap = 40 meters/minute.

The speed of the deer can be calculated using the formula speed = number of leaps per minute x distance covered per leap, which gives us speed = 4 leaps/minute x 5 meters/leap = 20 meters/minute.

The tiger is 50 leaps behind the deer, which is equivalent to a distance of 50 leaps x 8 meters/leap = 400 meters.

The relative speed of the tiger and deer is given as 20 meters/minute.

The time taken by the tiger to catch the deer can be calculated using the formula time = distance / speed, which gives us time = 400 meters / 20 meters/minute = 20 minutes.

The distance traveled by the tiger before it catches the deer can be calculated using the formula distance = speed x time, which gives us distance = 40 meters/minute x 20 minutes = 800 meters.

The time taken to reach the destination on schedule is given by the formula time = distance / speed, where distance is the distance to be traveled and speed is the speed at which the vehicle is traveling.

We are given two equations that relate the distance to be traveled, the speed at which the vehicle is traveling, and the time taken to reach the destination on schedule:

D/144 = D/S - 1/3

D/100 = D/S + 2/5

Subtracting the first equation from the second gives us the following equation:
44D/14400 = 11/15

Solving this equation for D gives us D = 14400 x 11/ 44 x 15 = 240.
Therefore, the distance D that the vehicle needs to travel in order to reach its destination on schedule is 240 kilometers.

using the formula for distance, which is distance = speed x time, to find the distance covered by each train in a given time period.

You are then setting the sum of the distances covered by both trains equal to the total distance between P and Q, 

which is 110 km. 

By solving this equation, you find that the trains meet after 3 hours, 

which means they meet at 10 a.m.

 using the formula for speed, which is speed = distance / time, to find the speed of the train in m/s.

You are then using this speed to find the length of the train, X, in meters. 

You do this by setting the distance covered by the train equal to the length of the train plus the distance between the two poles, 

which is 130 m. 

By solving this equation, you find that the length of the train is 203.3 meters.

The difference in distance covered in one week and two weeks is 84 - 42 = 42 miles
In one week, Giri jogs 42/7 = 6 miles/day
Thus, in two weeks, Giri jogs 6 x 7 = 42 miles/week
Hence, Giri jogs a total of 42 x 2 = 84 miles in two weeks.

Time taken to move the post = 8 s 
=> x/v = 8 
=> x = 8v --- (1)

Time taken to cross the platform 264 m long = 20 s
(x + 264)/v = 20
=> x + 264 = 20v ---(2)

Equation (1) represents the time it takes for the train to move past the post, which is 8 seconds. The distance the train travels in this time is given by x, which is the length of the train. The speed of the train is given by v, so x/v represents the time it takes for the train to move a distance x at a speed v. Setting this equal to 8 seconds allows you to solve for the speed of the train.

Equation (2) represents the time it takes for the train to cross the platform, which is 20 seconds. The distance the train travels in this time is given by x + 264, where x is the length of the train and 264 is the length of the platform. Setting this equal to 20v allows you to solve for the speed of the train.

You can then use these two equations to solve for the speed of the train by substituting the first equation into the second and solving for v. This gives you the final result of v = 22 m/s, or 79.2 km/hr.

Answer: B

Explanation: The original Roman calendar consisted of 10 months totaling 304 days.

Speed = distance/time = 600 meters / (5 minutes * (1 hour/60 minutes)) 

= 2 m/s 

= 2 * (18 km/hr / 5 m/s) 

= 7.2 km/hr.

Speed = distance/time 

= 1200 km / (5/3 hours) 

= 1200 km / (5/3 hours * (1 hour/60 minutes)) 

= 1200 km / (5/3 * (1 hour/60 minutes)) 

= 720 km/hr.

The required speed is 720 km/hr.

Calculate the increase in speed of an object that traveled a distance of 800 kilometers in 4 hours, starting at an initial speed of 80 km/hr. Here is the correct calculation:

Initial speed = 80 km/hr
Total distance = 80 * 10 = 800 km
New speed = distance/time = 800 km / 4 hours = 200 km/hr
Increase in speed = new speed - initial speed = 200 km/hr - 80 km/hr = 120 km/hr.

Distance = speed * time

For the first object:
Distance = S1 * T1 = 4 km/hr * 16/60 hr = 4/15 km = 2/7.5 km = 0.26666666666666666 km

For the second object:
Distance = S2 * T2 = 6 km/hr * 6/60 hr = 6/10 km = 3/5 km = 0.6 km

Total distance traveled = distance traveled by first object + distance traveled by second object = 0.26666666666666666 km + 0.6 km = 0.8666666666666667 km = 3 1/5 km.

Time taken to cover 600 km = distance/speed = 600 km / 100 km/hr = 6 hours
Number of stoppages = distance/stoppage interval - 1 = 600 km / 75 km - 1 = 7
Total time of stoppages = number of stoppages * duration of each stoppage = 7 * 3 minutes = 21 minutes
Total time taken = time taken to cover the distance + total time of stoppages = 6 hours + 21 minutes = 6 hours 21 minutes.

Distance traveled in first 2 hours = speed * time = 10 km/hr * 2 hours = 20 km

Distance traveled in next 1 hour = speed * time = 13 km/hr * 1 hour = 13 km

Total distance traveled = distance traveled in first 2 hours + distance traveled in next 1 hour = 20 km + 13 km = 33 km

Total time taken = time taken in first 2 hours + time taken in next 1 hour = 2 hours + 1 hour = 3 hours

Average speed = total distance traveled/total time taken = 33 km/ 3 hours = 11 km/hr.

Distance = 500 meters
Time = 4 minutes = 4 * 60 seconds = 240 seconds
Speed = distance/time = 500 meters / 240 seconds = 25/12 m/s

To convert the speed from m/s to km/hr, we use the conversion factor: 1 m/s = 18/5 km/hr

Speed in km/hr = (25/12 m/s) * (18/5 km/hr/m/s) 

= (25/12) * (18/5) 

= (225/60) = (45/12) 

= (5/12) * 9 = (5/4) 

= 7.5 km/hr.

Distance to be covered = Speed * Time = 140 km/hr * 2 hours = 280 km

Given that the distance to be covered is 280 kilometers and the time taken is 1 hour, 

the required speed is 280 km/hr.

Distance = 1500 meters
Time = 1 minute 20 seconds = 80 seconds

Required speed = distance/time = 1500 meters / 80 seconds = 75/4 m/s

To convert the speed from m/s to km/hr, we use the conversion factor: 1 m/s = 18/5 km/hr

Speed in km/hr = (75/4 m/s) * (18/5 km/hr/m/s) = (75/4) * (18/5) = (225/20) = (45/4) = 11.25 km/hr * (4/3) = 15/3 km/hr = 5 km/hr * 3 = 15 km/hr = 67.5 km/hr.

Distance = speed * time

To convert the speed from km/hr to m/s, we use the conversion factor: 1 km/hr = 5/18 m/s

Speed in m/s = 20 km/hr * (5/18 m/s/km/hr) = 50/9 m/s
Time = 2 minutes = 2 * 60 seconds = 120 seconds

Distance = speed * time = (50/9 m/s) * 120 seconds = 6000/9 meters = 666.6666666666667 meters.

The length of the bridge is 666.6666666666667 meters

Given that the distance traveled is 8 kilometers and the relative speed of the two boys is 2 km/hr, 

we can use the time formula to calculate the time taken:

Time = distance/speed = 8 km / 2 km/hr = 4 hours.

Given that the distance traveled is 14 kilometers and the speed is 8 km/hr, we can use the time formula to calculate the time taken:

Time = distance/speed = 14 km / 8 km/hr = 1 hour 45 minutes = 105/60 hours = 21/12 hours

To find the time required to cover the distance of 14 kilometers at a speed of 10 km/hr, we can use the time formula again:

Time = distance/speed = 14 km / 10 km/hr = 1.4 hours = 1.4 * 60 minutes = 84 minutes.

To find the speed of the horse to cover a distance of 40 kilometers in 30 minutes, you can use the speed formula:

Speed = distance/time = 40 km / (30 minutes * (1 hour/60 minutes)) 

= 40 km / (30/60) hours 

= 40 km / (1/2) hours 

= 40 km/hr * 2 

= 80 km/hr.

Given that the distance traveled is 150 kilometers and the speed is 60 km/hr, 

we can use the time formula to calculate the time taken:

Time = distance/speed = 150 km / 60 km/hr 

= 5/2 hours 

= 5/2 * 60 minutes 

= 150 minutes.

Distance = speed * time

We are given that the distance is X and the difference in speed is 4 km/hr. We can set up the equation as follows:

X/(6-8) = 4 km/hr

Solving for X, we get:

X = 4 km/hr * (6-8) = 4 km/hr * (-2) = -8 km

Since the distance cannot be negative, we can discard the negative solution and say that the distance traveled is X = 96 km.

Given that the bus covers a distance of 60 kilometers in an hour when it stops at bus stops and a distance of 65 kilometers in an hour when it does not stop at bus stops, 

we can calculate the time taken to cover 5 kilometers as follows:

Time = distance/speed = 5 km / (65 km/hr - 60 km/hr) 

= 5 km / 5 km/hr 

= 1/15 hour 

= 1/15 * 60 minutes 

= 4 minutes.

Given that the total distance between the two bus stations is 200 kilometers and that the buses cross each other at a distance of 120 kilometers from one of the stations, we can calculate the distance traveled by each bus as follows:

Distance traveled by first bus = 120 km

Distance traveled by second bus = 200 km - 120 km = 80 km

The ratio of the speeds of the two buses is equal to the ratio of the distances traveled by them. We can calculate the ratio of the speeds as follows:

Ratio of speeds = distance traveled by first bus / distance traveled by second bus 

= 120 km / 80 km 

= 3/2.

Distance covered in first half = Distance covered in second half

Distance covered in first half = speed * time→20*X=20X

Distance covered in second half = speed * time→25 * (5-X)

So, 20X = 25 * (5-X)

20X = 125 -25X

45X = 125

X= 125⁄45= 2.7 km

X is the distance covered in first half which is equal to the distance covered in the second half.

So to get the total journey we will multiply X with 2.

Total journey in Km = 2.7 x 2 = 5.4 km

Let X be the actual distance traveled by the man. 

We are given that the time is the same for both situations when the man runs at 20 km/hr and 24 km/hr. 

We can use this information to set up the following equation:

24X = 20X + 800

Solving for X, we get:

4X = 800
X = 800/4 = 200 km

Let X be the speed of the bus and car in some units. 

We are given that the speed of the car is 200/2 km/hr 

= 100 km/hr. 

We can use this information to solve for X:

6X = 100 km/hr

X = 100 km/hr / 6 = (50)/3 km/hr

The speed of the bus is 8X = 8 * (50)/3 km/hr 

= 400/3 km/hr 

= 133.33333333333334 km/hr.

Distance = Speed x Time
50 km = X * (6/9) * (5/3)
50 km = X * (10/9)

Solving for X, we get:

X = 50 km / (10/9) = 50 km * 9/10 = 45 km/hr.

The actual speed of the car is 45 km/hr.

Let T be the time it takes for Peter and Tom to meet. We are given that Peter's speed is 35 km/hr and Tom's speed is 735 km/hr. We can use this information to set up the following equations:

Distance traveled by Peter = Speed x Time = 35 km/hr * T
Distance traveled by Tom = Speed x Time = 735 km/hr * T

We are also given that the sum of the distances traveled by Peter and Tom is equal to the circumference of the track, which is 735 meters. We can set up the following equation:

Distance traveled by Peter + Distance traveled by Tom = Circumference of track
35T + 735T = 735 meters
770T = 735 meters
T = 735 meters / 770 = 189 seconds

The time it takes for Peter and Tom to meet is 189 seconds. We can convert this to minutes by dividing by 60 seconds per minute:

Time in minutes = 189 seconds / 60 seconds per minute = 3.15 minutes.

To find the average speed for the first 300 km of the journey, we need to calculate the total time it took for the man to travel the first 300 km and then divide the total distance traveled by the total time.

The man traveled the first 150 km of his journey at a speed of 80 km/hr, so it took him 150/80 = <<150/80=1.875>>1.875 hours.

He also traveled the next 150 km of his journey at a speed of 60 km/hr, so it took him 150/60 = <<150/60=2.5>>2.5 hours.

Therefore, the total time it took the man to travel the first 300 km of his journey was 1.875 + 2.5 = <<1.875+2.5=4.375>>4.375 hours.

The total distance traveled was 300 km, so the average speed was 300/4.375 = <<300/4.375=68>>68 km/hr. 

Average speed = 2ab/a+b = (2x80x100)/180 = 800/9 = 88 8/9km/hr

The speed of the river is X km/hr, and the man has a downward speed of 10 + X km/hr when he swims with the flow of the river, and an upward speed of 10 - X km/hr when he swims against the flow.

The problem states that the time it takes the man to cover a distance Y when he swims up the river is double the time it takes him to cover the same distance when he swims down the river.

To solve for the speed of the river, we can set up the following equation: Y/(10-X) = 2 * Y/(10+X)

We can then solve for X as follows:

10Y + XY = 20Y - 2XY
XY + 2XY = 20Y - 10Y
3XY = 10Y
3X = 10
X = 10/3 = <<10/3=3.333>>3.333 km/hr

Therefore, the speed of the river is approximately 3.333 km/hr.

Let X be the distance traveled on foot. The distance traveled on the bicycle is then 90 - X km.

Since the time taken to cover the total distance is equal to the sum of the time taken to cover the distances partly on foot and partly on the bicycle, we can set up the following equation: X/9 + (110 - X)/15 = 10

Solving for X, we get: 5X + 3(110 - X) = 45 * 10
5X + 330 - 3X = 450
2X = 450 - 330
2X = 120
X = 120/2 = 60

Therefore, the person traveled 60 km on foot.

Based on the information given, it looks like you are trying to find the distance between a village and a city. 

A person travels from the village to the city and back at a speed of 8 km/hr, and the total time taken for the round trip is 4 hours 45 minutes, or 285 minutes.

To find the total distance traveled, we can convert the time taken to hours by dividing by 60. 

The total time taken is 285/60 = 19/4 hours. The total distance traveled is then 8 * (19/4) = 38 km.

Since the person traveled from the village to the city and back, the distance between the village and the city is half of the total distance traveled, or 38/2 = 19 km.

 The man's speed when he returns from the office is X km/hr, and his speed when he goes to the office is 2/3X km/hr.

To find the average speed, we can add the speeds at which the man travels to and from the office and divide by 2. The average speed is then (X + 2/3X) / 2 = (5/3X) / 2 = 5/6X km/hr.

If the man's speed when he returns from the office is 30 km/hr, then his speed when he goes to the office is 2/3X = 2/3 * 30 = 20 km/hr.

The speed of one car is 5X km/hr, and the speed of the other car is 8X km/hr. 

The speed of the first car is 100 km/hr.

To find the value of X, we can set up the following equation: 5X = 100
Solving for X, we get: X = 100/5 = 20

The speed of the second car is 8X km/hr, so it is 8 * 20 = 160 km/hr.

The average speed of a vehicle is calculated by dividing the total distance traveled by the total time taken.

In this case, the total distance traveled is 80 km, and the total time taken is 75 minutes, or 75/60 hours. The average speed is then 80 / (75/60) = 64 km/hr.

For travelling 10 km he will take rest 9 times each of 4 minutes

So the total time taken to travell 10 km

=60 + 36

=96 minutes

To solve this problem, you can use the formula "distance = speed * time" to find the time it takes for the car to travel 500 meters at a speed of 30 km/hr.

First, you need to convert the speed from km/hr to m/s. You can do this by multiplying the speed by 1000 and dividing by 3600. This gives us: 30 km/hr = 30 * 1000 / 3600 = 8.333 m/s.

Next, you can plug the values into the formula to find the time it takes for the car to travel 500 meters:
time = 500 m / 8.333 m/s = 60 seconds.

To solve this problem, you can use the formula "speed = distance/time" to find the speed of the car.

The distance traveled is 800 meters, and the time taken is 260 seconds. Plugging these values into the formula gives us: speed = 800 m / 260 s = 3.07 m/s.

To convert the speed from m/s to km/hr, you can multiply it by (18/5). This gives us: 3.07 m/s * (18/5) = 11.05 km/hr.

To solve this problem, you can use the formula "distance = speed * time" to find the distance traveled by the car.

First, you need to convert the speed from km/hr to m/s. You can do this by multiplying the speed by 1000 and dividing by 3600. This gives us: 6 km/hr = 6 * 1000 / 3600 = 1.66 m/s.

Next, you need to convert the time from minutes to seconds. This gives us: 15 minutes = 15 * 60 seconds = 900 seconds.

Finally, you can plug the values into the formula to find the distance traveled: distance = 1.66 m/s * 900 s = 1500 meters.

SP/SQ = √tQ/√tP

SP and SQ are speeds of two the buses at points P and Q respectively.
tP = 18 hrs and tQ = 4 hrs
SP/SQ	=	√16/ √4

Therefore, ratio of speeds,

SP/SQ = 4/2

=2/1	

In this case, the total distance traveled is 1000 km, and the total time taken is 25 hours. The average speed is then 1000 km / 25 hours = 40 km/hr.

If you calculate the average speed using the formula "Average speed = Distance/Time", you will get: Average speed = (200 + 200 + 200 + 200) / (25/12) = 800 / (25/12) = 480 km/hr. 

The relationship between speed and time is inversely proportional, which means that as one increases, the other decreases.

In this case, the ratio of time is 5:5/3, which means that for every 5 units of time, there are 5/3 units of time. If we increase the ratio of time to 3:1, this means that for every 3 units of time, there is 1 unit of time.

Since speed is inversely proportional to time, this means that the ratio of speed is 1:3. This means that for every 1 unit of speed, there are 3 units of speed.

If the speed required is 320 km/hr, then the required speed to cover the distance in 3 units of time would be 320 km/hr * 3 = 960 km/hr.

To solve this problem, you can use the formula "distance = speed * time" to find the time it takes for the car to travel 100 meters at a speed of 36 km/hr.

First, you need to convert the speed from km/hr to m/s. You can do this by multiplying the speed by 1000 and dividing by 3600. This gives us: 36 km/hr = 36 * 1000 / 3600 = 10 m/s.

Next, you can plug the values into the formula to find the time it takes for the car to travel 100 meters: time = 100 m / 10 m/s = 10 seconds.