Question

A train takes 45 min to complete its 24 KM trip. It stops for 1 min at each of 7 stations during the trip.
(iii) Calculate the average speed of the train?
(iv) What would be the average speed if the stop at each station was reduced to 20 seconds?

Answer 1

Hint: At first calculating the average speed we have to find total time taken (without any stopping time) for completing a particular distance.
Thus, we have to find average speed by using the formula,
$s = \dfrac{d}{t}$ (s= speed, d=distance travelled, t=time elapsed.)

Complete step by step solution:
(iii)For the first portion,
There are total of 7 stations, so total 7 min are waste because of this, so completing 24 KM the train takes (45-7) min = 38 min
$\therefore $Now average distance $ = \dfrac{d}{t}$
$\begin{array}{l}
 = \dfrac{{24km}}{{38\min }}\\
 = \dfrac{{24 \times 60}}{{38}}Km/h\\
 = \dfrac{{720}}{{19}}Km/h\\
 = 37\dfrac{{17}}{{19}}Km/h
\end{array}$
(iv)For the second portion of the problem,
The stopping time reduces to 20 seconds.
So for 7 stations the total stopping time = $\left( {7 \times 20} \right) = 140$seconds $ = \dfrac{7}{3}\min $
So total time taken for 24 KM travel $ = \left( {45 - \dfrac{7}{3}} \right)\min $$ = 42\dfrac{2}{3}\min $
So now average speed
 $ = \dfrac{{24 \times 60}}{{42\dfrac{2}{3}}}km/h$
$ = \dfrac{{24 \times 60 \times 3}}{{128}}km/h$
$ = \dfrac{{135}}{4}km/h$$ = 33\dfrac{3}{4}km/h$

Note: - We have to be careful about the total time taken by the object for completing a particular distance. Because in this case some stopping time is included in the total time taken by the object so we have to subtract that extra time and then put the value in the formula of average speed and find the value.