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HELP

Vasily is flying his first solo trip. His plan is to fly round trip, 2368 miles. His flight plan factors in the wind speed of 20 miles per hour and expects that he will complete the flight in 7 hours.

At what speed is Vasily flying in still air? (Round your answer to the nearest mile per hour.)

Respuesta :

Let us assume that u be the speed of Vasily flying in still air. Since round trip is 2368 miles. One way will be 1184 miles.

On one side the wind speed will support Vasily and on the other side, the wind speed will oppose Vasily. Therefore, effective speeds for both the sides will be (u+20) and (u-20).

We can find the sum of times for both the sides and set the sum equal to 7 hours.

[tex]\frac{1184}{u+20}+\frac{1184}{u-20}=7[/tex]

Now, our next step is to solve this equation for u.

[tex]1184(u-20)+1184(u+20)=7(u+20)(u-20)[/tex]

[tex]1184u-23680+1184u+23680=7u^{2}-2800[/tex]

[tex]7u^{2}-2368u-2800=0[/tex]

[tex]u=339.46\text{ miles per hour}[/tex]

Therefore, Vasily is flying in still air at a speed of 340 miles per hour.