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?

simba.s Jan 11, 2020

#2**+3 **

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!

ElectricPavlov Jan 11, 2020