Two trains are moving in the same direction at the speed of 34 km/hr and 86 km/hr, their lengths are 300 metres and 480 metres respectively. What will be the time taken by faster train to cross the slower train?

Correct option is A

Given:

Speed of the slower train = 34 km/hr
Speed of the faster train = 86 km/hr
Length of the slower train = 300 m
Length of the faster train = 480 m

 Formula Used:
Relative speed when moving in the same direction = Difference in speeds
Time to cross =  $$\frac{\text{Total Length}}{\text{Relative Speed}}$$​​
Conversion from km/hr to m/s:$$\text { 1 km/hr} = \frac{5}{18} \text{ m/s}$$​
Solution:
​$$\text{Relative Speed} = 86 - 34 = 52 \, \text{km/hr}$$​​
Converting relative speed to m/s:

​$$\text{Relative Speed} = 52 \times \frac{5}{18} = \frac{260}{18} m/s$$​​
Total length to be covered = 300 + 480 = 780 m
​$$\text{Time} = \frac{780}{\frac{260}{18}} = 54 \, \text{seconds }$$​​
Thus, the time taken by the faster train to cross the slower train is 54 seconds.