Question

Two trains are running in the same directions at the speed of $60km/hr$ and $96km/hr$. If the faster train passes a man in the slower train in 20 seconds, then find the length of the faster train.

Answer 1

Hint: We first find the relative speed of the faster train. In crossing the man, the faster train actually crosses its own length. We convert the units from $km/hr$ to $m/\sec$ by multiplying with ${\displaystyle \frac{5}{18}}$. Then we multiply with the time 20 to find the final solution.

Complete step by step solution:
Two trains are running in the same directions at the speed of $60km/hr$ and $96km/hr$.
It is also given that the faster train passes a man in the slower train in 20 seconds.
The concept is of passing a moving object with respect to an object of negligible length. In that case the moving object actually passes the length of itself.
Now as the trains are running in the same directions, the speed of the train at which it crosses the man will be the relative speed.
Relative speed will also be the difference of the speeds as they are moving in the same direction which is $96-60=36km/hr$.
It crosses the man in 20 seconds. The relative speed is 36 kilometres in 1 hour.
We can transform the units from $km/hr$ to $m/\sec$ by multiplying with ${\displaystyle \frac{5}{18}}$.
Therefore, $36km/hr$ is equal to $36\times {\displaystyle \frac{5}{18}}=10m/\sec$.
In 20 seconds, it will cover $20\times 10=200$ metres which is the length of the faster train.
Therefore, the length of the faster train is 200 metres.

Note: In case the trains go in the opposite direction, the relative speed would have been the sum of the speeds instead of the subtraction. The speed of separation is the cumulative speed of those moving objects.