A boy goes from his home to school at a speed | vedclass

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(C) Let the distance between home and school be $S 	ext{ km}$.Time taken to go from home to school is $t_1 = \frac{S}{x} 	ext{ hours}$.Time taken to

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Let the distance between home and school be $S 	ext{ km}$.Time taken to go from home to school is $t_1 = \frac{S}{x} 	ext{ hours}$.Time taken to return from school to home is $t_2 = \frac{S}{y} 	ext{ hours}$.Average speed is defined as the total distance divided by the total time taken.Total distance $= S + S = 2S 	ext{ km}$.Total time $= \frac{S}{x} + \frac{S}{y} = S \left( \frac{1}{x} + \frac{1}{y} ight) = S \left( \frac{x + y}{xy} ight) 	ext{ hours}$.Average speed $= \frac{2S}{S \left( \frac{x + y}{xy} ight)} = \frac{2xy}{x + y} 	ext{ km/hr}$.

$A$ boy goes from his home to school at a speed of $x \text{ km/hr}$ and returns at a speed of $y \text{ km/hr}$. What is the average speed of the boy?

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