Question

In 1 hr, a plane can travel 390 mi into the wind and 470 mi with the wind. Find the wind speed and the rate of the plane in still air.

The wind speed is mph.
The rate of the plane in still air
mph

Answer 1

Let w be the wind speed and p the plane's speed in still air.

Flying against the wind, the plane has velocity

p - w = 390 mi/h

and flying with it, it has

p + w = 470 mi/h

Add the two equations together to eliminate w and solve for p :

(p - w) + (p + w) = 390 mi/h + 470 mi/h

2p = 860 mi/h

p = 430 mi/h

Subtract them to eliminate p and solve for w :

(p - w) - (p + w) = 390 mi/h - 470 mi/h

-2w = -80 mi/h

w = 40 mi/h