What is the length of the train ?

Question

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 sec respectively.

What is the length of the train ?

Answer 1

4kmph= 10/9 m/s
2kmph= 5/9 m/s
Let speed of train be s.
Relative speed × time = length of train
(s - 10/9) × 10= length

Also
(s - 5/9) × 9 = length

(s - 10/9) × 10 = (s - 5/9) × 9
s = 55/9

Length = (s - 10/9) × 10
= 50 metres

Ans: length of train is 50 metres