A plane flies from Alphaville to Betaville and then back to Alphaville. When there is no wind, the round trip takes 6 hours and 24 minutes, but when there is a wind blowing from Alphaville to Betaville at 50 miles per hour, the trip takes 6 hours and 40 minutes. How many miles is the distance from Alphaville to Betaville?
Rate x time = distance
distance/rate = time
d = distance roundtrip = 2d
2d/(r) = 6.4 hr 2d/6.4 = r = .3125 d = r Use this in the next equation
d/(r+50) + d/(r-50) = 6.667 hr
d/(.3125d +50) + d/(.3125d-50) = 6.667
.3125d^2 - 50d + .3125d^2 +50d = 6.667 ( .3125d+50)(.3125d-50)
.625 d^2 = 6.667(..097656d^2 - 2500)
-.02607 d^2 = -16667.5
d = ~ 800 miles
Round trip is 1600 miles
Check 1600/6.4 = 250 mph without wind
WITH wind 800/200 + 800/300 = 6.67 hr check!