Video Transcript
A train π΄ of length 90 meters was traveling at a speed of 170 kilometers per hour. It passed by another train π΅ of length 205 meters. Find the time required for train π΄ to completely pass train π΅, given that train π΅ is moving with a speed of 152 kilometers per hour in the same direction as train π΄.
Letβs begin by sketching a view from above, or birdβs-eye view, to model the scenario. We are told that train π΄ is 90 meters long and train π΅ is 205 meters long. The first train is traveling with a speed of 170 kilometers per hour, and the second train is traveling with a speed of 152 kilometers per hour in the same direction. We have been asked to find the time taken for train π΄ to completely pass train π΅.
We will do this using the fact that time is equal to distance divided by speed. And in this case, the total time will be equal to the total distance divided by the relative speed. As the two trains are moving in the same direction, we can calculate the speed of train π΄ relative to train π΅ by subtracting 152 from 170. We subtract the speed of train π΅ from the speed of train π΄, giving us 18 kilometers per hour.
Since the distance is given in meters, we need to convert the speed into the standard units of meters per second. We know that there are 1000 meters in one kilometer and 3600 seconds in one hour. This means that we can convert from kilometers per hour to meters per second by multiplying by 1000 and dividing by 3600. 18 kilometers per hour is therefore equal to five meters per second.
We can find the total distance traveled for train π΄ to completely pass train π΅ by adding the lengths of the two trains. 90 plus 205 is equal to 295, so the total distance is 295 meters.
We are now in a position to calculate the time required. We divide 295 meters by five meters per second. This is equal to 59 seconds. The time taken for train π΄ to completely pass train π΅ given that they are moving in the same direction is 59 seconds.
