A train crosses a pole in 15 secs, while it crosses 100 metre long railway…

Concept: When a train crosses a stationary point object such as a pole or a person, the distance it covers equals the train's own length, since the point object has no length of its own. When the train crosses an extended object such as a platform or a bridge, the distance covered equals the train's length plus the object's length. In every case, distance = speed x time.

Application:

1. Let the length of the train be L metres and its speed be v metres per second.

2. Crossing the pole: the train covers only its own length L in 15 seconds, so L = 15v.

3. Crossing the platform: the train covers its length plus 100 m in 25 seconds, so L + 100 = 25v.

4. Substituting L = 15v into the second equation: 15v + 100 = 25v.

5. Rearranging: 100 = 25v - 15v = 10v, so v = 10 m/s.

6. Substituting back: L = 15 x 10 = 150 m.

Cross-check: At a speed of 10 m/s, the train covers its own length of 150 m in 150 / 10 = 15 s, matching the pole-crossing time. It covers the length plus the platform, 150 + 100 = 250 m, in 250 / 10 = 25 s, matching the platform-crossing time. Both conditions are satisfied, confirming the length of the train is 150 m.