Question

A car travels from $A$ to $B$ at a speed of $20\text{km/h}$ and returns at a speed of $30\text{km/h}$. The average speed of the car for the whole journey is

• A. $25\text{km/h}$
• B. $24\text{km/h}$
• C. $50\text{km/h}$
• D. $5\text{km/h}$

Answer 1

The correct option is B $24\text{km/h}$

While going from $A$ to $B$, let the speed be $V_1$ and from $B$ to $A$ the speed be $V_2$.
$V_1=20km/h$
$V_2=30km/h$
If $d$ be the distance $AB$. Then we can say:
Time required for $A$ to $B=t_1=\frac{d}{V_1}$
Time required for $B$ to $A=t_2=\frac{d}{V_2}$

Average speed, $v=\frac{totaldistance}{totaltime}$
$v=\frac{d+d}{t_1+t_2}$
$v=\frac{2d}{\frac{d}{V_1}+\frac{d}{V_2}}$
$v=\frac{2V_1{V}_2}{V_1+V_2}$

$v=\frac{2\times 20\times 30}{20+30}$
$\Rightarrow v=24km/h$