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