Question & Answer
QUESTION

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

ANSWER Verified Verified
Hint:-In this problem first we need to determine the relative speed of slower trains with respect to faster one. Then we have to calculate the distance covered. And finally put these two (relative speed and distance covered) in formula\[{\text{ Required Time = }}\dfrac{{{\text{Distance covered}}}}{{{\text{Relative speed w}}{\text{.r}}{\text{.t to slower train}}}}\].

Complete step-by-step answer:
We know that relative speed is the speed of a moving body with respect to another. In this case relative speed with respect to slower train
 =$(45 + 30)$kmph
 =$75$kmph
On converting the relative speed into mps, we get
$
   \Rightarrow {\text{ }}\dfrac{{75 \times 1000}}{{36 \times 36}} \\
   \Rightarrow {\text{ }}\dfrac{{125}}{6} \\
 $
We have to find the time taken by the slower train to pass the driver of the faster train and not the complete train. So, distance covered= Length of slower train
Then, distance covered=$500{\text{ m}}$
\[\therefore {\text{ Required Time = }}\dfrac{{{\text{Distance covered}}}}{{{\text{Relative speed w}}{\text{.r}}{\text{.t to slower train}}}}\]
$
   \Rightarrow {\text{Required Time = (500}} \times \dfrac{6}{{125}}){\text{sec}}{\text{.}} \\
   \Rightarrow {\text{Required Time = 24 sec}}{\text{.}} \\
$
Hence, the time taken by the slower train to pass the driver of faster one is $24{\text{ sec}}{\text{.}}$
Note:- Whenever we get this type of question the key concept of solving is to have knowledge about relative speed and different time-distance relations . One thing to be remembered is that carefully convert the speed from kmph to mps by multiplying the speed in kmph with factor$\dfrac{{1000}}{{36 \times 36}}$ to get speed in mps.