Question

Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in the opposite direction on parallel tracks. What is the time (in seconds) which they will take to cross each other?
${\text{A}}{\text{.}}$ 9
${\text{B}}{\text{.}}$ 9.6
${\text{C}}{\text{.}}$ 10
${\text{D}}{\text{.}}$ 10.8

Answer 1

Hint: Here, we will proceed by finding the speeds of the given trains having unit m/s by using the formula that 1 km/hr = $\dfrac{5}{{18}}$ m/s. Then, we will find the relative speed between the two trains and use the formula $t = \dfrac{{{\text{Sum of the lengths of both the trains}}}}{{{\text{Relative speed between the trains}}}}$.

Complete Step-by-Step solution:
Given, Length of train A = 140 m
Length of train B = 160 m
As we know that 1 km/hr = $\dfrac{5}{{18}}$ m/s
Speed of train A = 60 km/hr = $60 \times \dfrac{5}{{18}} = \dfrac{{50}}{3}$ m/s
Speed of train B = 40 km/hr = $40 \times \dfrac{5}{{18}} = \dfrac{{100}}{9}$ m/s
Since, the trains A and B are running in the opposite directions on parallel tracks so the relative speed between these trains will be obtained by adding their individual speeds.
i.e., Relative speed between train A and train B = $\dfrac{{50}}{3} + \dfrac{{100}}{9} = \dfrac{{\left( {3 \times 50} \right) + 100}}{9} = \dfrac{{150 + 100}}{9} = \dfrac{{250}}{9}$ m/s
Since, Time taken = $\dfrac{{{\text{Distance covered}}}}{{{\text{Speed}}}}$
Also, we know that the formula for the time taken by two trains running in the opposite directions is given by
$t = \dfrac{{{\text{Sum of the lengths of both the trains}}}}{{{\text{Relative speed between the trains}}}}$
Required time taken = $\dfrac{{{\text{Length of train A }} + {\text{ Length of train B}}}}{{{\text{Relative speed between train A and train B}}}}$
$ \Rightarrow $Required time taken = $\dfrac{{140 + 160}}{{\left( {\dfrac{{{\text{250}}}}{9}} \right)}} = \dfrac{{300 \times 9}}{{250}} = \dfrac{{54}}{5} = 10.8$ s
Therefore, the time taken by the given two trains to cross each other is 10.8 seconds.
Hence, option D is correct.

Note: In this particular problem, we have converted the speed units from km/hr to m/s using the unit conversion formula because the lengths of the trains are given in unit metre (m) and the time which these trains will be taking to cross each other is asked in seconds (s). If the trains instead of running in the opposite direction were running in the same directions, we would have added the individual speeds of the trains to obtain the relative speed between the trains.