Question

A man standing on a railway platform
observes that a train going in one direction
takes 4 s to pass him. Another train of same
length going in the opposite direction takes
5 s to pass him. The time taken in seconds)
by the two trains to cross each other will be​

Answer 1

Answer:

Solution 40 seconds

because

s= d/t

let s1 be the speed of 1st train = d/4

let s2 be the speed of 2nd train = d/5

relative speed in same direction s= s1 - s2

= ( d/4 - d/5 )

= d/20

now t = d/s ( time taken to cross each other moving in same direction so d= 2d because 2 trains of same length d )

t =

$\frac{2d}{ \frac{d}{20} }$

=

$\frac{2d \times 20}{d}$

=40 sec

Thus the time taken to cross would be 40 seconds

Answer 2

Answer:

Let length of each train be X m, then

$$\eqalign{ & {S_1} = \frac{X}{4}\,{\text{and}} \cr & {S_2} = \frac{X}{5} \cr & {\text{Required time to cross each other,}} \cr & = {\frac{{2X}}{{ { {\frac{X}{4}} + {\frac{X}{5}} } }}} \cr & = \frac{{40}}{9}{\text{seconds}} \cr} $$