Question

A car completes the journey from $A$ to $B$ at a constant speed of $20km/hr$ and covers the return journey from $B$ to $A$ at a constant speed of $30km/hr$. The average speed for the total journey from $A$ to $B$ and back is

• A. $24km/hr$
• B. $\sqrt{600}km/hr$
• C. $25km/hr$
• D. $50km/hr$

Answer 1

The correct option is A $24km/hr$

Let the distance, $AB=S$

Speed for journey $A\to B$ is $v_1=20km/hr$

Speed for journey $B\to A$ is $v_2=30km/hr$

Time for distance $S$ will be $t=\frac{\text{distance}}{\text{speed}}$

Time for journey $A\to B$ is $t_1=\frac{S}{v_1}=\frac{S}{20}$

Time for journey $B\to A$ is $t_2=\frac{S}{v_2}=\frac{S}{30}$

Total distance for $A\to B$ then $B\to B$ is

$=AB+BA=S+S=2S$

Total time for $A\to B$ then $B\to B$ is

$=t_1+t_2$

So average speed $=\frac{Totaldistance}{Totaltime}=\frac{2S}{t_1+t_2}$

$=\frac{2S}{(\frac{S}{20}+\frac{S}{30})}$

$=\frac{2S\times 20\times 30}{S\times 50}$

$=24km/hr$