A plane can fly 540 miles with the wind in one hour less than it can fly 480 miles against the wind. The average wind speed is 30 miles per hour. Find the speed of the plane in still air.
A) 120 miles per hour
B) 150 miles per hour
C) 180 miles per hour
D) 210 miles per hour

Question

Quizplus · Accepted Answer

The speed of the plane in still air can be found by setting up equations based on the given information. Let the speed of the plane in still air be $p$ and the wind speed be $w = 30$ mph. When flying with the wind, the effective speed is $p + w$, and against the wind, it is $p - w$. The time to fly 540 miles with the wind is $540 / (p + 30)$, and the time to fly 480 miles against the wind is $480 / (p - 30)$. According to the problem, the time to fly with the wind is one hour less than the time to fly against it, so we have the equation $540 / (p + 30) + 1 = 480 / (p - 30)$. Solving this equation for $p$ gives us the speed of the plane in still air as 150 miles per hour.

A Plane Can Fly 540 Miles with the Wind in One