• # question_answer A boy runs for 10 minutes at a uniform speed of $\text{9 km }{{\text{h}}^{\text{-1}}}$. At what speed should he run for the next 20 minutes so that the average speed comes to$\text{12 km }{{\text{h}}^{\text{-1}}}$? A) $\text{13}\text{.5 km }{{\text{h}}^{\text{-1}}}$  B) $\text{10}\text{.2 km }{{\text{h}}^{\text{-1}}}$C)                $\text{8}\text{.2 km }{{\text{h}}^{\text{-1}}}$    D)        $\text{7}\text{.72 km }{{\text{h}}^{\text{-1}}}$

Let, the boy runs with speed v for next 20 min. Given that, Average speed$\text{= 12 km }{{\text{h}}^{\text{-1}}}$ As, average speed$\text{=}\frac{\text{Total distance covered }}{\text{Total time taken}}$ $\therefore \text{12=}\frac{\text{Total distance covered}}{\frac{(10+20)}{60}h}$ $\Rightarrow$Total distance covered $=12\times \frac{30}{60}=12\times \frac{1}{2}=6km$ Distance covered in 10 min $=9\times \frac{10}{60}=1.5km$ Remaining distance $=6-1.5=4.5km$ For next 20 min, he should run with speed $v=\frac{4.5}{20/60}=4.5\times 3=13.5\,\,km\,\,{{h}^{-1}}$