Question 331595: An airplane flew 3 hours with a 40 mph head wind. The return trip with a tail wind of the same speed took 2 hours. Find the speed of the plane in still air.
Answer by texttutoring(324)   (Show Source):
You can put this solution on YOUR website! When you have a headwind, you have to subtract the wind's speed from the plane's velocity, because it's slowing it down:
Let Vh = Velocity of plane with headwind, and Vp=Velocity of plane with no wind.
Vh = Vp - 40
Let Vt = Velocity of plane with tailwind
Vt = Vp + 40
We know that d=vt (d=distance, v=velocity (speed), and t=time) and also that the distance each way is exactly the same. Therefore we can set the Distances equal to each other:
D = D
Vt*time = Vh * time
(Vp+40)2 = (Vp-40)3
2Vp+80 = 3Vp -120
200 = Vp
So the speed of the plane in still air is 200mph.
Hope that helps. Let me know if you're still confused.
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