A train crosses a 180 m long platform in 20 seconds. It passes a man walking at 3.6 km/h in its own direction in 12 seconds. How long is the train?

Explanation

1. 01

   3.6 km/$h = 1$ m/s. Let the train's speed be $v$ m/s and its length $L$.

2. 02

   Platform: $L + 180 = 20v$. Man: $L = 12(v - 1)$.

3. 03

   So $20v - 180 = 12v - 12$, giving $8v = 168$ and $v = 21$ m/s.

4. 04

   $L = 12 \times 20 = 240$ m.