Question

Two goods train each 500 m long, and are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

Answer 1

Hint: To solve the question, we have to convert the given data of distance and speed into one system of units, since distance is given in metres and speed is given in kilometres per hour. We have to analyse that the question is to be solved to calculate the time taken by the slower train to pass the driver of the faster one which implies that the distance travelled will be equal to the length of the slower train. Thus, we can calculate the required answer by using the distance, relative speed and time formula.

Complete step-by-step answer:
We know that the time taken by the slower train to pass the driver of the faster one when the two trains are travelling in opposite directions of same length l and with speeds x, y such that x > y, is given by formula \[\dfrac{l}{x+y}\]
Where l is the distance travelled and x + y is the relative speed.
The given length of two goods trains is equal to 500 m long.
We know that 1 km = 1000 m. Thus, we get
\[500m=\dfrac{1\times 500}{1000}km=\dfrac{1}{2}=0.5.km\]
The given speeds of two goods trains are 45 km/hr and 30 km/hr.
By substituting the given values in the above mentioned formula, we get
The time taken by the slower train to pass the driver of the faster one
  \[\begin{align}
  & =\dfrac{0.5}{45+30} \\
 & =\dfrac{0.5}{75} \\
 & =\dfrac{0.5}{15\times 5} \\
 & =\dfrac{0.1}{15}hrs \\
\end{align}\]
 We know that 1 hour = 3600 sec. Thus, we get
\[\dfrac{0.1}{15}hrs=\dfrac{0.1}{15}\times 3600=0.1\times 240=24\sec \]
Thus, the time taken by the slower train to pass the driver of the faster one is equal to 24 seconds.

Note: The possibility of mistake can be, not converting the given data of distance and speed into one system of units, since distance is given in metres and speed is given in kilometres per hour. The other possibility of mistake can be, not analysing that the question did not ask for the time the two trains meet instead it asked for the time taken by the slower train to pass the driver of the faster one. Thus, the distance travelled will be equal to the length of the slower train not the sum of lengths of the two trains.