Question

A horse rider covers half the distance with $5\, m / s$ speed. The remaining part of the distance was travelled with speed $10\, m / s$ for half the time and with speed $15\, m / s$ 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

$t_{A B}=\frac{x}{5 m / s }$
In motion $BC$
$x = d _1+ d _2$
where $d _1 \& d _2$ we the distance travelled with $10 \,m / s$ and $15 \,m / s$ respectively in equal time intervals
$ \frac{ t ^{\prime}}{2} \text { each }$
$ d _1=\frac{10 t }{2}, d _2=\frac{15 t }{2}$
$ d _1+ d _2= x =\frac{ t }{2}(10+15)=\frac{25 t }{2}$
$< v >=\frac{2 x }{\frac{ x }{5}+\frac{2 x }{25}}=\frac{2 \times 25}{5+2}=\frac{50}{7} m / s$