College Math
posted by G .
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?

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/(x30)
they are equal, so
460/(x+30) = 310/(x30)
460(x30) = 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.
My answer is correct.