Question

A boy runs for $10\text{min}$ at a uniform speed of $9\text{km/h}$. At what speed should be run for the next $20\text{min},$ so that the average speed comes to $12\text{km/h}$?

• A. $10.5\text{km/h}$
• B. $12.5\text{km/h}$
• C. $13.5\text{km/h}$
• D. $11.5\text{km/h}$

Answer 1

The correct option is C $13.5\text{km/h}$

Total time of travel $=10\text{min}+20\text{min}=30\text{min}$
The average speed is $12\text{kmph}$
Using $s=vt$, the total distance covered in $30\text{min}$ with given average speed is $12\text{kmph}\times 30\text{min}=12\frac{km}{h}\times \frac{1}{2}h=6\text{km}$.
The distance covered in the first $10\text{min}$ is
$9\text{kmph}\times 10\text{min}=9\frac{km}{h}\times \frac{1}{6}h=1.5\text{km}$
Thus, he has to cover $6\text{km}-1.5\text{km}=4.5\text{km}$ in the next $20\text{min}$.
The speed required is
$\frac{4.5\text{km}}{20\text{min}}=\frac{4.5\text{km}}{\left(\frac{20}{60}\right)h}=13.5\text{kmph}.$