Answer
$15 $ mph
Work Step by Step
distance = (rate)$\times$(time) $\Rightarrow$ time = $\displaystyle \frac{\text{distance}}{\text{rate}}$
Let x be the rate of the bicyclist in calm air.
We are given:
$\displaystyle \frac{75}{x+10}=\frac{15}{x-10} \qquad$ ... $/\times(x+10)(x-10)$
$75(x-10)=15(x+10)$
$ 75x-750=15x+150\qquad$ ... add $750- 15x$
$ 60x=900\qquad$ ...$ /\div 60$
$x=15 $mph
rate of the bicyclist in calm air = $15 $ mph
