Problems on Trains

A train is not a point. To "cross" something it must clear its own length plus the length of the thing.

• A pole, a man, a signal post — no length of its own, so distance = length of the train.
• A platform, a bridge, a tunnel — distance = train + platform.
• Another train — distance = both lengths added.

For the speed, use relative speed:

• Opposite directions → add the speeds.
• Same direction → subtract them.

And always convert: km/h × 5/18 = m/s, because the lengths are in metres and the answer in seconds.

The single most common mistake is forgetting the train's own length on a platform question — dividing only the platform length by the speed. Fix it with a habit: write the distance as a sum before you divide, even when one of the two terms is zero.

A neat trick: if a train passes a pole in p seconds and a platform in q seconds, the extra q − p seconds were spent covering the platform alone. So speed = platform length ÷ (q − p), and then train length = speed × p. Two divisions, no algebra.

m/s = km/h × 5/18 · pole: t = L/v · platform: t = (L + P)/v · opposite: v₁ + v₂ · same direction: v₁ − v₂ · length from two times = P × p/(q − p)

A train 240 m long running at 54 km/h crosses a platform 360 m long. How long does it take? → Speed = 54 × 5/18 = 15 m/s. Distance = 240 + 360 = 600 m. Time = 600 ÷ 15 = 40 seconds. Sanity check: in 40 s at 15 m/s the train travels 600 m, which is exactly the train plus the platform; had you used only the platform you would have got 24 s, and the train would still be half on it.