Question

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

• A. $5km{h}^{-1}$
• B. $50km{h}^{-1}$
• C. $24km{h}^{-1}$
• D. $25km{h}^{-1}$

Answer 1

The correct option is C $24km{h}^{-1}$

Given:

Speed from point A to point B=30 km/h

Speed from point B to point A=20 km/h

Let the Distance between $A$ and $B$ be $x$
So, time taken from $A$ to $B=t_1=\frac{x}{30}$
time taken from $B$ to $A=t_2=\frac{x}{20}$
Total time $=t_1+t_2=\frac{x}{30}+\frac{x}{20}=\frac{5x}{60}$
Average speed $=\frac{totaldistance}{totaltime}=\frac{x+x}{\frac{5x}{60}}=\frac{2x}{\frac{5x}{60}}$
$\Rightarrow 24km{h}^{-1}$