A horse rider covers half the distance with 5 m/s speed. The remaining part of the distance was travelled with speed 10m/s for half the time and with speed 15m/s for other of the time. The mean speed of the rider averaged over the whole-time motion is $\frac{x}{7} m / s .$ The value of x is _______

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answer is 50.

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Detailed Solution

$\begin{array}{l} 25 t = y \Rightarrow t = \frac{y}{25} \\ ⟨ v ⟩ = \frac{distance}{time} = \frac{2 y}{(\frac{y}{5}) + 2 t} \\ = \frac{2 x}{(\frac{x}{5}) + (\frac{2 y}{25})} = \frac{50}{7} m / s \end{array}$

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