A short airplane trip between two cities took 30 minutes when traveling with the wind. The return trip took 45 minutes when traveling against the wind. If the speed of the plane with no wind is 320 mph, find the speed of the wind and the distance between the two cities (hint: pay attention to units).

Answer 1

speed of wind --- x mph

speed of plane going with the wind = 320 + x mph
speed of plane going against the wind = 320-x mph

distance with the wind = (320+x)(1/2)
distance against the wind = (320-x)(3/4)
but those are the same, so

(1/2)(320+x) = (3/4)(320-x)
times 4
2(320+x) = 3(320-x)
640 + 2x = 960 - 3x
5x = 320
x = 64

the speed of the wind is 64 mph
distance = (1/2)(320-x) = 128 miles

Answer 2

Thank you