Answer
$500 $ mph
Work Step by Step
distance = (rate)$\times$(time) $\Rightarrow$ time = $\displaystyle \frac{\text{distance}}{\text{rate}}$
Let x be the rate of the airplane in calm air.
We are given:
$\displaystyle \frac{2400}{x+100}=\frac{1600}{x-100} \qquad$ ... $/\times(x+100)(x-100)$
$2400(x-100)=1600(x+100)$
$ 2400x-240,000=1600x+160,000\qquad$ ... add $240000- 1600x$
$ 8000x=400,000\qquad$ ...$ /\div 8000$
$x=500 $mph
rate of the airplane in calm air = $500 $mph
