# Question Video: Finding the Time Needed by a Train Moving with Uniform Velocity to Pass Another Train Mathematics

A train A of length 65 m was moving at 74 km/h when it passed another train B of length 210 m traveling at 106 km/h in the other direction. How long did it take for train A to completely pass train B?

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### Video Transcript

A train A of length 65 meters was moving at 74 kilometers per hour when it passed another train B of length 210 meters traveling at 106 kilometers per hour in the other direction. How long did it take for train A to completely pass train B?

Let’s begin by sketching a diagram of this situation. Our diagram shows a bird’s eye view of the initial situation with the trains moving in the directions shown. We know that train A is 65 meters long and train B is 210 meters long. We also know that the velocity of train A is 74 kilometers per hour and the velocity of train B is 106 kilometers per hour. We need to calculate how long it takes for train A to completely pass train B. We can do this using our speed–distance–time triangle, where time is equal to distance over speed.

In this question, we will need to find the total distance traveled before train A has completely passed train B. This is simply equal to the total length of the two trains. As 65 plus 210 is equal to 275, the relative distance traveled will be 275 meters. The speed we need to calculate will be the relative velocity of train A with respect to train B. We can calculate this by subtracting the velocity of train B from the velocity of train A as the two trains are moving along the same one-dimensional axis.

Since train B is moving the opposite direction to train A, its velocity will be negative 106 kilometers per hour. 74 minus negative 106 is equal to 180. The velocity of train A relative to train B is 180 kilometers per hour. Since our distance is measured in meters and the speed in kilometers per hour, we will need to convert this to meters per second. We know that there are 1000 meters in one kilometer and 3600 seconds in one hour. We can therefore convert from kilometers per hour to meters per second by multiplying by 1000 and then dividing by 3600. This is the same as dividing by 3.6. 180 divided by 3.6 is equal to 50. Therefore, the relative velocity is 50 meters per second.

The time taken for train A to completely pass train B is therefore equal to 275 divided by 50. This is equal to 5.5 seconds.