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# Hi! I need help with solving this problem

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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?

Jan 11, 2020

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The distance works out to 1400 miles.

Jan 11, 2020
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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!

Jan 11, 2020
edited by ElectricPavlov  Jan 11, 2020