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

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Question

(C) Let the distance of the school from home be $d$.Let the time taken for the journey to school be $t_1$ and the time taken for the return journey be

Vedclass · Accepted Answer

$H.M.$

Vedclass · Answer

(C) Let the distance of the school from home be $d$.Let the time taken for the journey to school be $t_1$ and the time taken for the return journey be $t_2$.Therefore,$t_1 = \frac{d}{x}$ and $t_2 = \frac{d}{y}$.Average speed = $\frac{	ext{Total distance}}{	ext{Total time}} = \frac{d + d}{t_1 + t_2} = \frac{2d}{\frac{d}{x} + \frac{d}{y}}$.Simplifying the expression: $\frac{2d}{d(\frac{1}{x} + \frac{1}{y})} = \frac{2}{\frac{x+y}{xy}} = \frac{2xy}{x+y}$.This expression is the Harmonic Mean $(H.M.)$ of $x$ and $y$.

$A$ boy goes to school from his home at a speed of $x \text{ km/hour}$ and comes back at a speed of $y \text{ km/hour}$,then the average speed is given by

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