a plane travels 800 miles in 5 hours with the wind. it went the same distance in 8 hours when flying aginst the wind. find the rate of the wind

x = planes speed
y = wind speed

x +y = plane with wind
x-y = plane against wind

800 = 4(x+y)    4 hours to travel 800 miles with the wind

800 = 8(x-y)     8 hours to travel 800 miles against the wind

distribute the 2 formulas:

4x +4y = 800
8x -8y = 800

multiply 1st equation by 2 ( 8x +8y = 1600 )

add the 1st and 2nd equations:

8x + 8y = 1600
8x - 8y = 800

16x = 2400

divide both sides by 16

x = 2400 / 16

x = 150

use original 1st formula to solve for y ( wind speed)

4x +4y = 800
4(150) + 4y = 800
600 + 4y = 800

subtract 600 from each side:

4y = 200

divide both sides by 4

y = 200 / 4
y = 50

wind speed = 50 miles per hour