Question 1121629
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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 *[tex \Large r_w] represent the speed of the wind.  Relative to the direction of travel then, *[tex \Large -r_w] is the velocity of the wind relative to the aircraft when the aircraft is flying against the wind, aka upwind, and *[tex \Large +r_w] 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:  *[tex \Large 350\ +\ r_w] and the speed of the aircraft upwind is then: *[tex \Large 350\ -\ r_w].


Since distance equals rate (aka speed) times time:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (350\ -\ r_w)t\ =\ 145]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (350\ +\ r_w)t\ =\ 205]


Which is to say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  t\ =\ \frac{145}{350\ -\ r_w}]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  t\ =\ \frac{205}{350\ +\ r_w}]


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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{145}{350\ -\ r_w}\ =\ \frac{205}{350\ +\ r_w}]


Solve for *[tex \Large r_w]


Which is the wind speed.  The direction is up to you to discover if you can.
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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