Question

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.

Which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? Recall the formula d = rt.

Answer 1

Using d = rt:

With the wind (tailwind): 120 = (x + y)(0.75)
Against the wind (headwind): 120 = (x − y)(1)

Equivalently:
x + y = 160
x − y = 120

(From these, x = 140 mph and y = 20 mph.)