Mountain Biking

We use the following formula/information

$Time = \displaystyle\frac{Distance}{Rate}$ , $\hspace{1cm}$ $T_{total} = T_{up} + T_{down} = 6$ .

If we let $x$ be the normal rate, then $T_{up} = \frac{96}{x-16}$ and $T_{down} = \frac{96}{x+8}$

Thus we have:

$T_{total} = T_{up} + T_{down} = \frac{96}{x-16} + \frac{96}{x+8} =96\{\frac{1}{x-16} + \frac{1}{x+8}\}= 6.$

This equation gives us: $\frac{x+ 8 + x - 16}{x^2-8x - 128} = \frac{6}{96}$

After cross multiplying, and some simplification, we arrive at

$x^2 - 40x = 0$ or equivalently $x (x-40) = 0$ . This gives us the normal rate $x = 40$ .

assume normal speed is x so 96 /(x-16) +96/(x+8) =6 from this equation x=40

A round trip takes 6 hr. so ,in options 40 is that by which we can find 40-16 = 24km/h is the speed upward and 40+8 = 48km/h is the downward speed so it takes (96/24)+96/48)= 6 hours...simple