Train problems are time-speed-distance problems where the train's own length must be covered. Convert speeds carefully between km/hr and m/s, and use relative speed when two bodies move.
1Unit conversion
a km/hr = a × 5/18 m/s
a m/s = a × 18/5 km/hr
2Crossing objects
Time to pass a pole, a man standing still or a signal post = length of train ÷ speed
Time to pass a platform, bridge or tunnel of length b = (length of train + b) ÷ speed
Example
A 150 m train at 54 km/hr passes a pole in 150 ÷ 15 = 10 s and a 300 m platform in 450 ÷ 15 = 30 s.
3Relative speed
Same direction: relative speed = u − v
Opposite directions: relative speed = u + v
Two trains of lengths a and b cross each other in (a + b) ÷ relative speed
4Meeting after crossing
If two trains start at the same time from A and B towards each other and take a and b seconds to reach the other end after meeting, then (speed of A) : (speed of B) = √b : √a