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4.Average
medium
A cyclist goes from a place to another and returns by the same route. He pedals his way uniformly with speed $u$ while going and with speed $v$ while returning. The average speed of his journey is
A
$\frac{u+v}{2}$
B
$\frac{u-v}{2}$
C
$\frac{1}{\frac{1}{2}\left(\frac{1}{u}+\frac{1}{v}\right)}$
D
$\frac{1}{\frac{1}{2}\left(\frac{1}{u}-\frac{1}{v}\right)}$
Solution
Let one way distance be $'x'.$
Total distance $=2 x$
Total time taken $=\left(\frac{x}{u}+\frac{x}{v}\right)$
Average speed $=\frac{\frac{2 x}{x}+\frac{x}{v}}{u}=\frac{1}{\frac{1}{2}\left(\frac{1}{u}+\frac{1}{v}\right)}$
Standard 13
Quantitative Aptitude
