The speed of a train is 72 km/h and it crosses a platform in 25 seconds. If…

Concept

To compare the time a train takes to pass different objects, convert all speeds to m/s and use Distance = Speed x Time. When a train passes a moving object travelling in the SAME direction, the relevant speed is the relative speed (train speed minus object speed). When it passes a point object (a person), the distance covered equals the train's own length; when it passes a platform, the distance covered equals train length plus platform length.

Application

1. Convert speeds: train 72 km/h = 72 x 5/18 = 20 m/s; athlete 18 km/h = 18 x 5/18 = 5 m/s.

2. Athlete runs in the same direction, so relative speed = 20 - 5 = 15 m/s.

3. Crossing the athlete (a point) covers exactly the train's length: length = relative speed x time = 15 x 10 = 150 m.

4. Crossing the platform, the train moves at its own 20 m/s for 25 s, covering 20 x 25 = 500 m, which equals train length + platform length.

5. Platform length = 500 - 150 = 350 m.

Cross-check

Reverse it: a 150 m train plus a 350 m platform is 500 m; at 20 m/s that takes 500/20 = 25 s, matching the given crossing time. So the platform is 350 m.