A plane flies 500 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is $24 \mathrm{mph}$, what is the speed of the plane in still air?
A) $126 \mathrm{mph}$
B) $136 \mathrm{mph}$
C) $141 \mathrm{mph}$
D) $161 \mathrm{mph}$

Question

Quizplus · Accepted Answer

Let the speed of the plane in still air be $x$ mph. When flying with the wind, the plane's speed is $x + 24$ mph, and against the wind, it's $x - 24$ mph. Since the times for both parts of the trip are the same, we can set up the equation $\frac{500}{x + 24} = \frac{350}{x - 24}$. Solving this equation for $x$ gives the speed of the plane in still air as $136$ mph.

A Plane Flies 500 Miles with the Wind and 350 24mph24 \mathrm{mph}24mph

A Plane Flies 500 Miles with the Wind and 350 $24 \mathrm{mph}$