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A body covers a certain distance x in equal thirds - the first third of distance with speed v$_1$, the second third with a speed of v$_2$ and the last third with a speed of v$_3$. What is the average speed of the body over time?

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Answer: $\large\frac{3v_1v_2v_3}{v_2v_3+v_1v_3 + v_1v_2}$
In general terms, the time taken to cover a third of the distance $x$ with speed $v$ is $t = \large\frac{\text{x}/3}{\text{v}}$
$\Rightarrow$ the overall speed $ \overline{v} = \Large\frac{x}{ \frac{x}{3v_1} + \frac{x}{3v_2} + \frac{x}{3v_3}}$
$\Rightarrow \overline{v} = \large\frac{3v_1v_2v_3}{v_2v_3+v_1v_3 + v_1v_2}$
answered Aug 11, 2014 by balaji.thirumalai

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