Question

A person travels up hill at an average speed of (u - v) km/hr and comes down the hill back at an average speed of (u + v) km/hr. His average speed for the whole journey is ___________________.

• A. u km/hr
• B. $\frac{u^2-v^2}{u}km/hr$
• C. $\sqrt{u^2-v^2}km/hr$
• D. $\frac{u}{u^2-v^2}km/hr$

Answer 1

The correct option is B $\frac{u^2-v^2}{u}km/hr$

Let the distance of the hill be d

then time taken totravel uphill $t_1=\frac{d}{u-v}\left(1\right)$

Time taken to travel down the hill $t_2=\frac{d}{u+v}-\left(2\right)$

Total time $t=t_1+t_2$

$t=\frac{d}{u-v}+\frac{d}{u+v}$

$t=d\left(\frac{2u}{u^2-v^2}\right)$

Average speed =$\frac{totaldistance}{totaltime}$

=$\frac{2d}{d(\frac{2u}{u^2-v^2}})$

=$\frac{u^2-v^2}{u}$ Km/h