SOLUTION: An airplane took 2 hours to fly 600 km against a head wind. The retrun trip with the wind took 1 and two thirds hours. Find the speed of the plane in stll air.

Question 188935: An airplane took 2 hours to fly 600 km against a head wind. The retrun trip with the wind took 1 and two thirds hours. Find the speed of the plane in stll air.
Answer by jonvaliente(64) (Show Source): You can put this solution on YOUR website!
Let x=speed of the plane in still air
y=speed of the head wind
distance=speed * time
Against the head wind, the speed of the plane is x-y:
(x-y)*2=600 (1)
With the wind, the speed of the plane is x+y:
(x+y)*(5/3)=600 (2)
Simplifying (1) and (2) we get:
2x-2y=600 (1)
(5/3)x+(5/3)y=600 (2)
Equating (1) and (2)
2x-2y=(5/3)x+(5/3)y
Multiply both sides by 3
(2x-2y)*3=((5/3)x+(5/3)y)*3
6x-6y=5x+5y
Solving for x we get:
x=11y (3)
Substituting 11y for x in (1) we get:

((11y)-y)*2=600
10y*2=600
20y=600
y=30
Solving for x using (3)
x=11(30)
x=330
The speed of the plane in still air is 330kph

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