A car moves from X to Y with a uniform speed $v_{u}$ and returns to Y with a uniform speed $v_{d}$ . The average speed for this round trip is

\frac{2 v_{d} v_{u}}{v_{d} + v_{u}}

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\sqrt{v_{u} v_{d}}

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\frac{v_{d} v_{u}}{v_{d} + v_{u}}

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\frac{v_{u} + v_{d}}{2}

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Solution

The correct option is A $\frac{2 v_{d} v_{u}}{v_{d} + v_{u}}$
Average speed is always given by $\frac{T o t a l d i s t a n c e}{T o t a l t i m e}$

Let's assume that distance between $X$ and $Y$ is $d$
So, time taken to go from $X$ to $Y$ will be $\frac{d}{v_{u}}$
And time taken to go from $Y$ to $X$ will be $\frac{d}{v_{d}}$
So, average speed will be $\frac{2 d}{\frac{d}{v_{u}} + \frac{d}{v_{d}}}$ $= \frac{2 v_{d} v_{u}}{v_{d} + v_{u}}$

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