Question

A car travels first half distance between two places 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. $120\text{km/h}$
• B. $90\text{km/h}$
• C. $60\text{km/h}$
• D. $180\text{km/h}$

Answer 1

The correct option is D $180\text{km/h}$

Let the total distance be 2D
For first half distance $D$:
$\text{Time taken}=\frac{\text{Distance}}{\text{Average speed}}=\frac{D}{60}$
For the later half distance $D$, let the average speed be $v$
Time taken =$\frac{D}{v}$
For total journey:
$\text{Total distance}=\text{Average speed}\times \text{Time}$ $\Rightarrow 2D=90\times (\frac{D}{60}+\frac{D}{v})$
On Solving, $v=180\text{km/h}$