Question

A car travels first half distance with uniform speed of $60\text{km/hr}$. What should be its uniform speed (in $\text{km/hr}$) for the second half of the distance so that its average speed over the entire journey becomes $90\text{km/hr}$.

• A. $120$
• B. $150$
• C. $180$
• D. $210$

Answer 1

The correct option is C $180$

Let the total distance travelled by the car over entire journey be $2D.$
For first half distance $D$:
$\text{Time taken}=\frac{\text{Distance}}{\text{Average speed}}=\frac{D}{60}$
For the latter half distance $D$, let the average speed be $v$
Time taken $=\frac{D}{v}$
For total journey:
$\text{Total distance}=\text{Average speed}\times \text{Total Time}$
$2D=90\times (\frac{D}{60}+\frac{D}{v})$
$\Rightarrow \frac{D}{45}=\frac{D}{60}+\frac{D}{v}$
$\Rightarrow \frac{1}{v}=\frac{1}{45}-\frac{1}{60}$
$\therefore v=180\text{km/h}$