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A man flies a small airplane from fargo to bismarck, north dakota—a distance of 180 mi. because he is flying into a head wind, the trip takes him 2 h. on the way back, the wind is still blowing at the same speed, so the return trip takes only 1 h 15 min. what is his speed in still air, and how fast is the wind blowing?

Respuesta :

when plane is moving in head wind condition we will have

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

[tex]V_{plane} - v_{wind} = \frac{180}{2}[/tex]

[tex]V_{plane} - v_{wind} = 90 mph[/tex]

now when wind is tail wind condition during return journey we will have

time = 1 h 15 min = 1.25 hour

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

[tex]V_{plane} + v_{wind} = \frac{180}{1.25 }[/tex]

[tex]V_{plane} + v_{wind} = 144 mph[/tex]

Now add both equations

[tex]V_{plane} = 117 mph[/tex]

[tex]v_{wind} = 27 mph[/tex]

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