SOLUTION: An airplane took 2 hours to fly 600 km against a head wind. The return trip with the wind took 1 2/3 hours. Find the speed of the plane in still air.

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Question 26425: An airplane took 2 hours to fly 600 km against a head wind. The return trip with the wind took 1 2/3 hours. Find the speed of the plane in still air.
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the speed of the plane be y
Let the speed of the wind be x
1 2/3 = 5/3
Against = -
With = +

2(x-y)=600 ------>2x-2y=600 (solve for y)
x-y=300
y=300+x (subsitution)

%285%28x%2By%29%29%2F3=600---->5x%2F3%2B5y%2F3=600 apply subsitution.
5x%2F3%2B%285%28300%2Bx%29%29%2F3=600
5x%2F3%2B%281500%2B5x%29%2F3=600 ---> Remove the fraction by multipling the equation by 3.
3%285x%2F3%29%2B3%28%281500%2B5x%29%2F3%29=3%28600%2F1%29
5x+1500+5x=1800
10x=300
x=30
y=300+(30)
y=330

Hence, the speed of the wind is 30 mph and the speed of the plane is 330 mph (in still air).
Paul.