A vehicle travels half the distance L with speed $v_{1}$ and the other half with speed $v_{2}$ , then its average speed is

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$\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

$\frac{2 v_{1} + v_{2}}{v_{1} + v_{2}}$

$\frac{v_{1} + v_{2}}{2}$

$\frac{L (v_{1} + v_{2})}{v_{1} v_{2}}$

answer is C.

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Detailed Solution

$S_{1} = S_{2} = \frac{L}{2}$
$Average speed = \frac{L}{t_{1} + t_{2}} = \frac{L}{\frac{L}{2 v_{1}} + \frac{L}{2 v_{2}}}$
$\frac{L}{(\frac{L}{2}) (\frac{1}{v_{1}} + \frac{1}{v_{2}})} = \frac{2 v_{1} v_{2}}{v_{1} + v_{1}}$

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