Question

A pilot can fly an airplane 2240 miles with the wind in the same time as she can fly 1920 miles against the wind. If the speed of the wind is 40 mph, find the speed of the plane in still air.

Answer 1

Recall your d = rt, distance = rate * time

so... hmm if the plane has a still air speed of say "r", when it's going with the wind, is not really going "r" fast, is going "r + 40 ", because the wind is adding 40mph to its speed, is really moving.

and when the plane is going against the wind, is not really going "r" fast either, is going " r - 40 ", because the wind is eroding speed from it.

now, it went 2240 miles for say "t" hours, and it did 1920 miles for the same length of time, "t" hours.

$\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ \textit{with the wind}&2240&r+40&t\\ \textit{against the wind}&1920&r-40&t \end{array} \\\\\\ \begin{cases} 2240=(r+40)t\implies \frac{2240}{r+40}=\boxed{t}\\ 1920=(r-40)t\\ ----------\\ 1920=(r-40)\left( \boxed{\frac{2240}{r+40}} \right) \end{cases} \\\\\\ 1920=\cfrac{(r-40)2240}{r+40}\implies 1920(r+40)=(r-40)2240 \\\\\\ 1920r+76800=2240r-89600\implies 166400=320r \\\\\\ \cfrac{166400}{320}=r$

and surely you know how much that is.