SOLUTION: A plane can fly 350 mph in still air. If it can fly 205 miles downwind in the same amount of time it can fly 145 miles upwind, find the velocity of the wind.

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Question 1121683: A plane can fly 350 mph in still air. If it can fly 205 miles downwind in the same amount of time it can fly 145 miles upwind, find the velocity of the wind.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


You cannot find the velocity of the wind with the given information because you have no idea of which direction the wind is blowing. Velocity is a vector quantity which means that it has both a magnitude (what we generally refer to as "speed") and a direction. "50 mph" is a speed. "50 mph North" is a velocity. Be that as it may, you can express the velocity of the wind relative to the direction of travel of the aircraft, whatever that might be.

Let represent the speed of the wind. Relative to the direction of travel then, is the velocity of the wind relative to the aircraft when the aircraft is flying against the wind, aka upwind, and is the velocity of the wind relative to the aircraft when the aircraft is flying with the wind, aka downwind.

The speed of the aircraft downwind is then: and the speed of the aircraft upwind is then: .

Since distance equals rate (aka speed) times time:



and



Which is to say:



and



But since the problem says "in the same amount of time":



Solve for

Which is the wind speed. The direction is up to you to discover if you can.


John

My calculator said it, I believe it, that settles it
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