Question

A boy goes to school from his home at a speed of $x$ km/hr. and comes back at a speed of $y$ km/hr. then the average speed of the boy is

• A. $\frac{x+y}{2}km/hr$
• B. $\sqrt{xy}km/hr$
• C. $\frac{2xy}{x+y}km/hr$
• D. $\frac{x+y}{2xy}km/hr$

Answer 1

Answer: (C)

$\frac{2xy}{x+y}km/hr$

Let the distance between home and school $=S$ km
Time taken to reach school from home $=\frac{S}{x}$ hr.
Time consumed to reach home from school $=\frac{S}{y}$ hr
$\text{Average speed}=\frac{\text{Total distance}}{\text{Total time taken}}$
$=\frac{S+S}{\frac{S}{x}+\frac{S}{y}}$
$=\frac{2}{\frac{1}{x}+\frac{1}{y}}$
$=\frac{2xy}{x+y}$ km/hr.