Question

A plane traveled 2565 miles with the wind in 4.5 hours and 2205 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.

Answer 1

• plane: 530 mi/h
• wind: 40 mi/h

Explanation:

Let p and w represent the speeds of the plane and the wind. The relation between time, speed, and distance is ...

speed = distance/time

p +w = (2565 mi)/(4.5 h) = 570 mi/h

p -w = (2205 mi)/(4.5 h) = 490 mi/h

Adding these speeds, we get ...

(p +w) +(p -w) = (570) +(490) mi/h

2p = 1060 mi/h

p = 530 mi/h

Then the speed of the wind is ...

w = 570 mi/h -p = (570 -530) mi/h = 40 mi/h

The plane's speed is 530 mi/h; the wind speed is 40 mi/h.