# algebra

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An airplane flying with the wind can cover a certain distance in a = 3 hours. The return trip against the wind takes b = 4.5 hours. How fast is the plane and what is the speed of the wind, if the one-way distance is c = 720 miles?

• algebra -

speed of plane in no wind --- x mph
speed of wind ---- y mph

time with the wind = 720/(x+y) = 3
3x + 3y = 720
x + y = 240

time against the wind = 720/(x-y) = 4
4x - 4y = 720
x-y = 180

2x = 420
x = 210
back in x+y=240
210 + y = 240
y = 30

the plane has a speed of 210 mph, and the wind was 30 mph

• algebra -

You are smart! Thanks!

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