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When a plane flies with the​ wind, it can travel 1575 miles in 3.5 hours. when the plane flies in the opposite​ direction, against the​ wind, it takes 4.5 hours to fly the same distance. find the average velocity of the plane in still air and the average velocity of the wind?

Respuesta :

When plane is flying along the wind then we can say

[tex]V_{plane} + v_{wind} = \frac{distance}{time}[/tex]

[tex]V_{plane} + v_{wind} = \frac{1575}{3.5}[/tex]

[tex]V_{plane} + v_{wind} = 450 mph[/tex]

Now when its going against the wind the speed is given by

[tex]V_{plane} - v_{wind} = \frac{distance}{time}[/tex]

[tex]V_{plane} - v_{wind} = \frac{1575}{4.5}[/tex]

[tex]V_{plane} - v_{wind} = 350 mph[/tex]

Now by the above two equations we will have

[tex]V_{plane} = 400 mph[/tex]

[tex]v_{wind} = 50 mph[/tex]

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