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# A train 125m long passes a man running at 5kmph in the same direction in which the train is going in 10 seconds. Find the speed of the train (in kmph).

Last updated date: 19th Mar 2023
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Hint: Assume the speed of the train to be x kmph. Calculate the speed of the train relative to the man. As the man is a point object, we can consider that the train covers the distance equal to its length in the given time, which is 10 seconds. Solve the equation formed by relating speed of train with distance covered by train and time taken to travel the distance, to get the value of speed of train.

We have a 125m long train which passes a man running at a speed of 5kmph in the same direction in which the train is going in 10 seconds. We have to calculate the speed of the train.
Let’s assume that the speed of the train is x kmph.
So, the speed of the train relative to man will be $x-5$ kmph.
Considering the man as a point object, we observe that the train covers a distance equal to its own length in 10 seconds. Thus, the train covers a distance of 125m in 10 seconds by running at a speed of $x-5$ kmph.
We know that speed of an object is the ratio of distance covered by an object to the time taken by the object to cover that distance.
Thus, we have speed of the train $=x-5kmph=\dfrac{125}{10}m/\sec =12.5m/\sec$.
We have to convert the speed of the train in $m/\sec$ to kmph.
We know that $1m/\sec =3.6kmph$.
To convert x $m/\sec$ into kmph, we will multiply x by 3.6.
Thus, we have $12.5m/\sec =12.5\times 3.6kmph=45kmph$.
So, we have $x-5kmph=45kmph$.
$\Rightarrow x=45+5=50kmph$
Hence, the speed of the train is 50kmph.

Note: It’s very necessary to keep the units of speed, distance and time in mind. If we solve the question without keeping the units the same on both sides of the equation, we will get an incorrect answer. We can also solve the question by considering the speed of man relative to speed of train and then solving equations to get the speed of train.