SOLUTION: A one engine plane can fly 120 mph in still air. If it can fly 490 miles with a tailwind in the same time that it can fly 350 miles against a headwind, what is the speed of the win

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Question 1154139: A one engine plane can fly 120 mph in still air. If it can fly 490 miles with a tailwind in the same time that it can fly 350 miles against a headwind, what is the speed of the wind?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let "v" be the speed of the wind.


Then the effective speeds of the plane are   120+v  mph  tailwind  and  120-v  against the headwind.


Therefore, the "time" equation is

    490%2F%28120%2Bv%29 = 350%2F%28120-v%29


First, cancel the common factor 70 in both sides; then cross multiply. You will get

    7*(120-v) = 5*(120+v)

    840 - 7v  = 600 + 5v

    840 - 600 = 5v + 7v

    240       = 12v

      v       = 240/12 = 20.


ANSWER.  Speed of wind is 20 miles per hour.