Question

A train 110 meters long is running with a speed of 60kmph. In what time will it pass a man who is running at 6kmph in the direction opposite to that in which the train is going?
(a). 5 sec
(b). 6 sec
(c). 7 sec
(d). 10 sec

Answer 1

Hint:-The most important formula that we use in solving this question would be the relation between speed, distance and time which is given as follows
\[distance=speed\times time\]
Now, as the train and the man are moving in the opposite direction, then the net speed of them would be equal to (60+6) kmph that is 66kmph.

Complete step-by-step solution -
As mentioned in the question, we have to find the time in which the train will pass the man who is running in the opposite direction to the train.
Now, we know that as the train and the man are moving in opposite directions, the net speed would become 66kmph as mentioned in the hint.
Now, as we know the net speed for the motion and we also know the distance that is to be travelled that is the entire length of the train, so, we can use the relation given in the hint to solve this question as follows
 \[\begin{align}
  & distance=speed\times time \\
 & \dfrac{110}{1000}=66\times time \\
 & time=\dfrac{110}{66}\times \dfrac{1}{1000} \\
 & time=\dfrac{10}{6000}=\dfrac{1}{600}hr \\
 & time=\dfrac{1}{600}\times 60\times 60\sec =6\sec \\
 & \\
\end{align}\]
Hence, the time taken by the train to cross the man is 6 sec.

Note: -The students can make an error if they don’t know the relation between speed, distance and time which is given in the hint as follows
The most important formula that would used in solving this question would be the relation between speed, distance and time which is given as follows
\[distance=speed\times time\]