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Airplane with Tailwind and Headwind

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Q: 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.

A: 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 with tailwind) = Vh * (time with headwind)

(Vp+40)2 = (Vp-40)3
2Vp+80 = 3Vp -120
200 = Vp

So the speed of the plane in still air is 200 mph.

Hope that helps. Let me know if you’re still confused.