Question

A bus travelling the first one-third distance at a speed of $10\text{km/h},$ the next one-third at $20\text{km/h}$ and the last one-third at $60\text{km/h}$. The average speed of the bus is

• A. $24\text{km/h}$
• B. $18\text{km/h}$
• C. $30\text{km/h}$
• D. $42\text{km/h}$

Answer 1

The correct option is B $18\text{km/h}$

Let total distance covered by the car be $d$
So, we have, average speed as
$v_{avg}=\frac{\text{Total distance}}{\text{Total time}}$
So, for $1/3^{rd}$ distance, time taken is given by
$t_1=\frac{d}{3\times 10}=\frac{d}{30}\text{hr}$
for next $1/3^{rd}$ distance, time taken is given by
$t_2=\frac{d}{3\times 20}=\frac{d}{60}\text{hr}$
Similarly, for next $1/3^{rd}$ distance, time taken is given by
$t_3=\frac{d}{3\times 60}=\frac{d}{180}\text{hr}$
So, total time taken is $t_1+t_2+t_3=\frac{d}{30}+\frac{d}{60}+\frac{d}{180}=\frac{d}{18}$
Thus, average speed is given by
$v_{avg}=\frac{d}{\frac{d}{18}}=18\text{km/h}$