Question

A car travelled the first one-third of the distance $d$ at a speed of $20km{h}^{-1}$, the second one-third of the distance at a speed of $40km{h}^{-1}$ and the last one-third of the distance at a speed of $120km{h}^{-1}$. Determine the average speed of the car.

• A. $18km/h$
• B. $27km/h$
• C. $36km/h$
• D. $45km/h$

Answer 1

The correct option is C $36km/h$

We know that $\text{speed}=\frac{\text{distance travelled}}{\text{time taken}}$

Time taken by the car to travel first one-third of the distance $=\frac{\frac{d}{3}}{20}$
Time taken by the car to travel second one-third of the distance $=\frac{\frac{d}{3}}{40}$
Time taken by the car to travel last one-third of the distance $=\frac{\frac{d}{3}}{120}$

$\text{Average speed}=\frac{\text{Total distance travelled}}{\text{Total time taken}}$

$\Rightarrow \text{Average speed}=\frac{\frac{d}{3}+\frac{d}{3}+\frac{d}{3}}{\frac{\frac{d}{3}}{20}+\frac{\frac{d}{3}}{40}+\frac{\frac{d}{3}}{120}}$
$=\frac{d}{\frac{d}{60}+\frac{d}{120}+\frac{d}{360}}$
$=36km/h$