Question

A long-distance train is scheduled to reach its destination in $19$ hours. After $10$ hours of journey, due to disruption of rail traffic, the train has to be stationed for $1$ hour. If the average speed of the train is $100$km/hr, at what speed should it travel to cover the distance in same amount of time?

Answer 1

Step 1: Finding total distance travelled in $19$ hours

Total journey time = $19$ hours

The train has completed a $10$-hour journey.

The average speed of train is $100km/hr$.

So, the total distance in $19$ hours at a speed of $100km/hr$ is $=19\times 100=1900kms$

Step 2: Finding new average speed.

The train has moved for $10$ hours.

So it has completed a distance in $10$ hours $=10\times 100=1,000km$

Due to rail traffic it had to wait for few hours

So the train completed the distance of$1000km$ in $11hours$.

Remaining distance$=1900-1000=900km$

Remaining times $19hours-11hours=8hours$

New average speed $\begin{array}{rcl}& =& \frac{Dis\tan ce}{Time}\end{array}$
$\begin{array}{rcl}& =& \frac{900}{8}\\ & =& 112.5km/h\end{array}$

Hence, the train had to move with a speed of $112.5km/h$ to complete the journey in the same time (to cover the delay).