Question

A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
A. 3.6 sec
B. 18 sec
C. 36 sec
D. 72 sec

Answer 1

Hint:To find the solution of this question, we should know about the concept of relative speed, that is if two objects move in the same direction, then the relative speed is calculated as their difference. So, we will calculate the relative speed of the train with respect to the man as 45 - 9 = 36 kmph and then we will calculate the time taken by the train to cross the jogger using the formula, $\text{speed}=\dfrac{\text{distance}}{\text{time}}$.

Complete step-by-step answer:
In this question, we have been asked to find the time taken by the train to pass the jogger when it is given that the jogger’s speed is 9 kmph and the train’s speed is 45 kmph and the jogger is 240 m ahead of a 120 m long train. To solve this question, we should know about relative speed, which is the speed of one object with respect to the other and when both the objects are moving in the same direction, then their difference is taken as their relative speed. So, we can say that the relative speed of the train with respect to the jogger is, speed of train - speed of jogger. So, we get,
Relative speed of train = (45 - 9) kmph = 36 kmph.
So, if we consider the relative speed of the train as the original speed, then we have to assume that the jogger is standing. So, we can say that the train must travel a distance of (240 + 120) m = 360 m as the front of the engine and the jogger are 240 m apart and the engine is 120 m long.
Now, we know that 1 km = 1000 m and 1 hr = 3600 sec. So, we can say that, 36 kmph = $36\times \dfrac{1000}{3600}=10$ mpsec.
We know that speed, distance, and time are related as, $\text{speed}=\dfrac{\text{distance}}{\text{time}}$.
It can also be written as, $\text{time}=\dfrac{\text{distance}}{\text{speed}}$.
Now, we know that the train has to travel 360 m with a speed of 10 mpsec. So, we can say that,
Time taken = $\dfrac{360}{10}\Rightarrow 36\sec $.
Hence, we can say that a 120 m long train with a speed of 45 kmph at a distance of 240 m from a jogger who is running at a speed of 9 kmph will cross the jogger in 36 sec.
Therefore, the correct option is option C.

Note: The possible mistakes we can make while solving this question by not converting the speed of the train and the jogger into mpsec, because of which we can loose marks. We can also think of solving this question by finding the relative speed of the man with respect to the train, which is absolutely a correct way, but it will make the solution complicated because of the negative sign as we would get (9 - 45) kmph = -36 kmph and the chances of error would increase.