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

The correct answer is 50.

tAB​=$\frac{x}{5m/s}$
In motion BC
x=d1​+d2​
where d1​&d2​ we the distance travelled with 10 m/s and 15m/s respectively in equal time intervals
2t′​ each
d1​=$\frac{10t}{2}$​,d2​=$\frac{15t}{2}$
d1​+d2​=x=$\frac{t}{2}$(10+15)=$\frac{25t}{2}$
v=$\frac{2x}{\frac{x}{5}+\frac{2x}{25}}$​=750​m/s