Question

A moving train of length 'L' metres crosses a man 9.5
standing on a platform and a bridge 450 metres long
in 4 seconds and 19 seconds respectively. What will
be the time takeny by the train to cross a paltform 430
m long?​

Answer 1

given, Length of the train is L.

let speed of the train is x m/s

train crosses a man standing on a platform in 4sec.

so, time taken to cross the man = length of train/speed of train

or, 4 = L/x ......(1)

again, train crosses a bridge 450 long in 19sec.

so, time taken to cross the bridge = (length of train + length of bridge)/speed of train

or, 19 = (L + 450)/x

or, 19 = L/x + 450/x

from equation (1),

or, 19 = 4 + 450/x

or, 15 = 450/x

or, x = 30 m/s

putting x = 30 in equation (1),

so, 4 = L/30 ⇒ L = 120m

hence, length of train = 120m

now, we have to find time taken to cross a platform of length 430 m

so, time taken = (length of train + length of platform)/speed of train

= (120 + 430)/30

= 550/30

= 55/3

= 18.33 sec