Question

A truck travelled the first one-third of the distance $d$ at a speed of $10{\text{kmh}}^{-1}$, the second one-third of the distance at a speed of $12{\text{kmh}}^{-1}$ and the last one-third of the distance at a speed of $20{\text{kmh}}^{-1}$. The average speed of the truck is approximately equal to (in ${\text{kmh}}^{-1}$)

• A. $10$
• B. $13$
• C. $15$
• D. $17$

Answer 1

The correct option is B $13$

Using
$\text{speed}=\frac{\text{distance travelled}}{\text{time taken}}$
Time taken to travel first one-third of the distance $=\frac{\frac{d}{3}}{10}$
Time taken to travel second one-third of the distance $=\frac{\frac{d}{3}}{12}$
Time taken to travel last one-third of the distance $=\frac{\frac{d}{3}}{20}$
$\Rightarrow \text{Average speed}=\frac{\frac{d}{3}+\frac{d}{3}+\frac{d}{3}}{\frac{\frac{d}{3}}{10}+\frac{\frac{d}{3}}{12}+\frac{\frac{d}{3}}{20}}$
$=\frac{d}{\frac{d}{30}+\frac{d}{36}+\frac{d}{60}}=\frac{360}{28}=12.8\text{km/h}\approx 13\text{km/h}$