An aircraft travels with the wind for 120 miles in 0.75 of an hour. The return trip is flown against the wind and takes exactly 1 hour.

Answer 1

120 = (p + w)(0.75)

120 = (p - w)(1)

Can you solve for either p or w and aswer?

Answer 2

Let x = the speed of the plane in still air.

Let y = the speed of the wind

Then the speed of the plane against the wind is x - y and with the wind, x + y

The distance traveled with or against the wind is the same and is 120 miles

Using, Rate x Time = Distance traveled we get the following 2 equations:

Against the wind: (x - y) (.75) = 120 and with the wind (x + y)(1) = 120

1. (x - y)(.75) = 120 or dividing both sides by .75 or 3/4, the equation simplifies to x - y = 160
2. (x + y)(1) = 120 or x + y = 120

Adding both eliminates y: x - y = 160

x + y = 120

2x = 280

Divide by 2 and x = 140 mph which is the speed of the plane.

To find the speed of the wind, replace x with 140 in either equation and y is 20 mph.