# College Math

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A plane flies 460 miles with the wind and 310 miles against the wind in the same length of time. If the speed of the wind is 30 mph, what is the speed of the plane in calm air?

• College Math -

speed of plane in calm air --- x mph

time to go 460 miles with the wind = 460/(x+30)
time to go 310 miles against the wind = 310/(x-30)

they are equal, so
460/(x+30) = 310/(x-30)
460(x-30) = 310(x+30)
460x - 13800 = 210x + 9300
150x = 23100
x = 154

the speed of the plane is 154 mph

check:
speed with the wind = 184
time of trip against wind = 460/184 = 2.5 hours
speed against wind = 124 mph
time of trip against wind = 310/124 = 2.5 hours.

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