With a tailwind a plane can fly 450 miles in 3 hours The ret

With a tailwind, a plane can fly 450 miles in 3 hours. The return trip takes 5 hours Find the speed of ther plane in still air and the speed of the wind.

Solution

Let the speed of the plane be x
Let the speed of the wind be y
3(x+y)=450---------->3x+3y=450
Solve for y
3y=450-3x
y=150-x (subsituion)

Second equation:
5(x-y)=450 ----->5x-5y=450 (use subsitution)
5x-5(150-x)=450
5x+5x-750=450
10x=1200
x=120

3(120)+3y=450
360+3y=450
3y=90
y=30


Hence, the speed of the plane is 120mph and the speed of the wind is 30mph.