Question

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

Answer 1

Answer: 50

$t_{AB}=\frac{x}{5m/s}$
In motion $BC$
$x=d_1+d_2$
where $d_1\&d_2$ we the distance travelled with $10m/s$ and $15m/s$ respectively in equal time intervals
$\frac{t^{\prime }}{2}\text{ each }$
$d_1=\frac{10t}{2},d_2=\frac{15t}{2}$
$d_1+d_2=x=\frac{t}{2}(10+15)=\frac{25t}{2}$
$<v>=\frac{2x}{\frac{x}{5}+\frac{2x}{25}}=\frac{2\times 25}{5+2}=\frac{50}{7}m/s$