Answer
The speed of the plane in still air is $520$ miles per hour and the speed of the wind is $40$ miles per hour.
Work Step by Step
The plane traveled $2520$ miles with the wind in $4.5$ hours and $2160$ miles against the wind in the same amount of time.
Speed of the plane with the wind: $\frac{2520}{4.5} = 560$ miles per hour
Speed of the plane against the wind: $\frac{2160}{4.5} = 480$ miles per hour
Let $p$ be the speed of the plane in still air in miles per hour and let $w$ be the speed of the wind in miles per hour.
$p + w = 560$ Equation $(1)$
$p - w = 480$ Equation $(2)$
Equation $(1)$ + Equation $(2)$
$2p = 1040$
$p=520$
Substitute $p$ into Equation $(1)$.
$520 + w = 560$
$w=40$
The speed of the plane in still air is $520$ miles per hour and the speed of the wind is $40$ miles per hour.
