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.

0.75(x + y) = 120
x − y = 120
0.75(x − y)= 120
x + y = 120
120(x + y) = 0.75
120(x − y) = 1
120(x − y) = 0.75
120(x + y) = 1

Answer 1

With wind: distance = rate * time => 120 = (x + y)(0.75) so 0.75(x + y) = 120.
Against wind: 120 = (x − y)(1) so x − y = 120.

Thus the system is
0.75(x + y) = 120
x − y = 120

(Equivalently x + y = 160 and x − y = 120, giving x = 140 mph, y = 20 mph.)