A horse rider covers half the distance with $5 \mathrm{~m~s}^{-1}$ speed. The remaining part of the distance was travelled with speed $10 \mathrm{~m~s}^{-1}$ for half the time and with speed $15 \mathrm{~m~s}^{-1}$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $\frac{x}{7} \mathrm{~m~s}^{-1}$. The value of $x$ is $\_\_\_\_$.