Answer

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**Hint**

Determine the distance between two trains using the total distance and the interval between the departure times of two trains. This same distance will have to be covered at a lower speed and the time to cover this distance will determine the time intervals between arrivals of the trains.

Formula used:

$v = \dfrac{d}{t}$ where $v$ is the velocity of an object, $d$ is the distance travelled by the object, and $t$ is the time taken to cover this distance.

**Complete step by step answer**

We’ve been given that the speed of the trains $ = {\text{ }}80{\text{ }}kmph$ and they arrive at regular intervals of $10{\text{ mins = 1/6 hour}}$. Then we can calculate the distance between 2 successive trains as:

$d = vt $

$ = 80 \times \dfrac{1}{6} $

$ = \dfrac{{40}}{3}km $

Now when the speed of all the trains is reduced to ${\text{v' = 50 }}kmph$, the distance between 2 successive trains remains the same however the time required by the trains to cover this distance will increase. As a result, the time between arrivals of trains will also increase. We can calculate this time interval $t'$ as:

$t' = \dfrac{d}{{v'}}$

$t' = \dfrac{{40}}{{3 \times 50}} = \dfrac{4}{{15}}hr$

Hence the time interval between the arrival of trails during the defect in the rails is $4/15\,hr$ or equivalently$\dfrac{4}{{15}} \times 60 = 16\,{\text{mins}}$.

**Note**

The tricky part in this question is breaking the problem down to a single formula as the distance between the trains remains constant because they all travel at the same speed. As a result, the time interval between the arrivals of 2 successive trains will only depend on the change in velocity.

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