Trains

(1) Distance = Speed × Time
Speed = Distance/Time
Time = Distance/Speed

(2) Convert kilometres per hour (km/hr) to metres per second (m/s)
X km/hr = X × 5/18 m/s

(3) Convert metres per second (m/s) to kilometres per hour (km/hr)
X m/s = X × 18/5 km/hr

Problems on Trains

(1) Time taken by a train x meters long in passing a signal post or a pole or a standing man is the same as the time taken by the train to cross 'x' meters with its own speed.

(2) Time taken by a train 'x' meters long in passing a stationary object of length 'y' meters is the same as the time taken by the train to cover (x + y) meters with its own speed.

(3) Suppose two trains or bodies are moving in the same directions at 'u' km/hr and 'v' km/hr such that u > v, then their relative speed = (u - v) km/hr.
If two trains of lengths 'x' km and 'y' km move in the same direction at 'u' km/hr and 'v' km/hr (where u > v), then time taken by them to cross each other is hrs.

(4) Suppose two trains or bodies are moving in the opposite directions at 'u' km/hr and 'v' km/hr. Then, relative speed = (u + v) km/hr.
If two trains of length 'x' km and 'y' km move in the opposite directions at 'u' km/ph and 'v' km/pr, then time taken to cross each other =

(5) If two trains start at the same time from stations A and B towards each other and after crossing, they take 'a' & 'b' hours in reaching B and A respectively. Then,
A's speed : B's speed = ().

Example: A train 100 m long is running with a speed of 70 km/hr. In what time will it pass a man who is running at 10 km/hr in the same direction in which the train is going?

Speed of train relative to man = (70 - 10) kmph = .Time taken by the train to cross the man = Time taken by it to cover 100 m at m/sec. = seconds = 6 seconds.