an airplane flies 450 miles with the wind and 300 against th

an airplane flies 450 miles with the wind and 300 against the wind in the same length of time. If the speed of the wind is 40 mph, what is the speed of the airplane in still air?

Solution

450 miles with the wind = 450/(x+40)
300 against the wind = 300/(x-40)
450/(x+40) = 300/(x-40)
multiply each side by (x+40)(x-40)
450(x-40) = 300(x+40)
450x - 18,000 = 300x + 12,000
450x - 18,000 - 300x = 300x + 12,000 - 300x
150x - 18,000 + 18,000 = 12,000 + 18,000
150x = 30,000
divide each side by 150
x = 200
The speed of the airplane in still air is 200 mph
check:
450/(200+40) = 300/(200-40)
450/(240) = 300/(160)
15/8 = 15/8