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 seconds respectively.
What is the length of the train?

Answer 1

The length of the train is 49.9 meters.
Let L be the length of the train
The person walking at 2 KMPH would travel 5 meters in 9 seconds (2000*9/3600). So, in overtaking that man, the train would have traveled L+5 meters in 9 seconds.
The person walking at 4 KMPH would travel 11.1 meters in 10 seconds (4000*10/3600). In overtaking that man, the train would have travelled L+11.1 meters in 10 seconds.
If the train is traveling at a constant speed,
(L+5)/9 = (L+11.1)/10
10*(L+5) = 9*(L+11.1)
10L + 50 = 9L + 99.9
10L-9L = 99.9 - 50 = 49.9 meters

Answer 2

S1=2kmph=2*5/18m/s=5/9m/s
S2=4kmph=4*5/18m/s=10/9m/s
Let's length of train is x meters and speed y m/s
Relative speeds of train with persons are
(y-5/9) & (y-10/9)
Then,
(1) x/(y-5/9)=9
=> x=9y-5..............................(i)
(2) x/(y-10/9)=10
=>10(9y-10)=9x
=>90y-9x=100...................(ii)
By solving (i) & (ii) we get x=50
so length of the train is 50 m