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.
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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