Question

Two men are walking towards each other alongside a railway track. A freight train overtakes one of them in 20 seconds and exactly 10 minutes later meets the other man coming from the opposite direction.
The train passes this man is 18 seconds. Assume the velocities are constant throughout. How long after the train has passed the second man will the two men meet?​

Answer 1

Let ‘L’ be the length of train, ‘x’ be the speed of the first man,

‘y’ be the speed of the second man and

‘z’ be the speed of the train.

20=

1

(z−x)

and 18=

1

(z+y)

⇒ z=10x+9y

Distance between the two men =600(z+y) mt

Time =

600(z+y)−600(x+y)

(x+y)

=

600(9x+9y)

(x+y)

= 90 minutes

Answer 2

The two men will meet 90 minutes after the train has passed the second man

Given,

train overtakes the first man in 20 seconds

train travels for 10 minutes before it reaches the second man

train passes the second man in 18 seconds

velocities are constant throughout

To Find,

Time taken for the two men to meet, after the train has passed the second man

Solution,

This can be solved using a simple logic

Let L be the length of the train

x be the velocity of the first man

y be the velocity of the second man

z be the velocity of the train

We are given that the two men are walking toward each other

It is given that the train passes the first man in 20 seconds

Here, the first man and the train are traveling in the same direction

Therefore, $20=\frac{L}{z-x}$ ⇒ $L = 20(z-x)$

It is also given that the train passes the second man in 18 seconds

Here, the second man and the train are traveling in the same direction

Therefore, $18=\frac{L}{z+y}$⇒ $L = 18(z+y)$

From the two equations, we get $z=10x+9y$

Distance between the two men, [distance = speed x time]

= $600(z+y)$ meters, as 10 mins = 600 seconds

Also, after 10 minutes, the distance between them will be $600(x+y)$, as both of them are walking towards each other in this time span also

Hence, the current distance between both of them will be:

$D = \frac{600(z+y)-600(x+y)}{x+y}$

$D = \frac{600(z+y-x-y)}{x+y}$

$D = \frac{600(z-x)}{x+y}$

$D = \frac{600(10x+9y-x)}{x+y}$

$D = \frac{600(9x+9y)}{x+y}$

$D = \frac{5400(x+y)}{x+y}$

D = 5400 seconds

D = 90 mins

Therefore, the two men are 90 minutes apart