Question

A train travels from city A to city B with a constant speed of 10 $m{s}^{-1}$ and return back to city A with a constant speed of 20 $m{s}^{-1}$. Find its average speed during its entire journey.

• A. $25m/s$
• B. $\frac{40}{3}m/s$
• C. $\frac{20}{3}m/s$
• D. $20m/s$

Answer 1

The correct option is B

$\frac{40}{3}m/s$

Average speed is always calculated from the ratio of total distance to the total time taken. Average speed is not the arithmetic average of speeds in a journey.
Consider, the distance between the two cities A and B = x m.
Time taken by the train to travel from A to B $=\frac{x}{10}=t_1\left(say\right)$
Time taken to come back from B to A $=\frac{x}{20}=t_2\left(say\right)$
$\therefore$ Average speed $=\frac{Totaldistance}{Totaltime}=\frac{x+x}{t_1+t_2}=\frac{2x}{\frac{x}{10}+\frac{x}{20}}$
$=\frac{40}{3}m/s$