Two trains X and Y are moving in the same direction and completely cross each other in 84 seconds. Their speeds are 81 km/h and 63 km/h respectively. If Train Y is 40 metres longer than Train X, find the length of Train Y.

ATQ,
As both trains are moving in the same direction, their relative speed will be the difference of their speeds.
Relative speed = 81 − 63 = 18 km/h
Convert 18 km/h into m/s:
18 km/h = (18 × 5/18) m/s = 5 m/s
Time taken to cross each other = 84 seconds
Distance covered while crossing = Relative speed × Time
= 5 × 84
= 420 metres
This distance is equal to the sum of the lengths of both trains.
Let the length of Train X be x metres.
Then the length of Train Y = x + 40 metres.
So,
x + (x + 40) = 420
2x + 40 = 420
2x = 380
x = 190
Length of Train Y = 190 + 40 = 230 metres