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

Answer 1

The correct option is C $180$

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 :
$\text{Total distance}=\text{Average speed}\times \text{total time}$
$2D=90(\frac{D}{60}+\frac{D}{v})$
On Solving , $v=180\text{km/hr}$