Question

A motorcyclist drives from $A$ to $B$ with a uniform speed of $30km{h}^{-1}$ and returns with a speed of $20km{h}^{-1}.$ Find his average speed.

Answer 1

Let distance from $A$ to $B$ is $dkm$
time taken from $A$ to $B$
$t_1=\frac{d}{30}$
time taken from $B$ to $A$
$t_2=\frac{d}{20}$
total time $t=t_1+t_2$
$=\frac{d}{30}+\frac{d}{20}$
$=\frac{d}{10}\left[\frac{1}{3}+\frac{1}{2}\right]=\frac{d}{10}\left[\frac{3+2}{6}\right]$
$t=\frac{d}{10}\times \frac{5}{6}$
$t=\frac{d}{12}$
$\text{average speed}=\frac{\text{total distance}}{\text{total time}}$
$=\frac{d+d}{\frac{d}{12}}$
$=\frac{2d\times 12}{d}$
$=24km/h$