Question

Two trains 120m and 80m in length are travelling in opposite directions with velocities
42 kmh–1 and 30 kmh–1 respectively. How much time will they require to completely cross
each other?

Answer 1

You need to use the concept of relative velocity here. The relative velocity in this case will be 42+30 as both the trains are running in opp direction. Also the distance needed to be traveled will be 120+80=200 m = 0.2 Km.

Time = Distance/Speed = 0.2/72 = 0.0027 Hr = 10 Seconds

Answer 2

$\large\underline{\sf{Given- }}$

Two trains 120m and 80m in length are travelling in opposite directions with velocities 42 km per hour and 30 km per hour respectively.

$\large\underline{\sf{To\:Find - }}$

How much time will they require to completely cross each other?

$\large\underline{\sf{Solution-}}$

Given that,

☆ Length of first train, x = 120 m = 0.12 km

☆Speed of first train, a = 42 km per hour.

☆ Length of second train, y = 80 m = 0.08 km

☆Speed of second train, b = 30 km per hour.

Since,

Both the train travelling in opposite directions, so relative speed of the train = 42 + 30 = 72 km per hour

Total length of train = 0.12 + 0.08 = 0.2 km

Let assume that time taken by them to across each other completely is 't' hours.

We know,

$\boxed{ \rm{ Time = \frac{Distance}{Speed}}}$

So, on substituting the values, we get

$\rm :\longmapsto\:t = \dfrac{0.2}{72} \: hours$

$\rm :\longmapsto\:t = \dfrac{2}{720} \times 60 \: minutes$

$\rm :\longmapsto\:t = \dfrac{1}{6} \: minutes$

$\rm :\longmapsto\:t = \dfrac{1}{6} \times 60 \: seconds$

$\rm :\longmapsto\:t = 10 \: seconds$

So, Time taken by two trains to across each other completely is 10 seconds.

Short Cut trick :-

1. If the length of two trains be x km and y km and speed of the trains be a km per hour and b km per hour in opposite directions, where ( a > b ), then time taken by them to across each other is

$\boxed{ \rm{ t \: = \: \frac{x + y}{a + b}}}$

2. If the length of two trains be x km and y km and speed of the trains be a km per hour and y km per hour in same directions, where ( a > b ), then time taken by them to across each other is

$\boxed{ \rm{ t \: = \: \frac{x + y}{a - b}}}$