The distance from Detroit, MI to Paris, France is approximately 3930 mi. Flying from Detroit to Paris takes 8 hr with the jet stream. The return flight takes 8.3 hr since the plane is flying against the jet stream.
a. The speed of the plane in still air, rounded to the nearest whole number, is
b. The speed of the jet stream, rounded to the nearest whole number, is

The speed of the plane in still air is approx 482 miles per hour(mph). The speed of the jet stream, rounded to the nearest whole number, is 9 mph

How does air stream affects speed of flight?

Flight speed in air stream = Flight speed in still air + effect of air stream

If the flight is going opposit, then:

Flight speed in air stream = Flight speed in still air - speed of air stream

If the flight is going along with flight, then:

Flight speed in air stream = Flight speed in still air + speed of air stream

For this case, we're specified that:

Distance from Detroid to Paris is approx 3930 miles
Time it takes by flight along the air stream = 8 hours
Time it takes by flight against the air stream = 8.3 hours

Speed of flight along the stream is:

[tex]S = \dfrac{\delta D}{\delta T} = \dfrac{3930}{8} = 491.25 \: \rm mph[/tex]

Speed of flight against the stream is:

[tex]S = \dfrac{\delta D}{\delta T} = \dfrac{3930}{8.3} \approx 473.49 \: \rm mph[/tex]

Let the speed of air stream be y, and that of the flight in still air be x miles per hour, then we get:

Along air stream:

[tex]x + y =491.25\\[/tex] (in miles per hour)

and Against the stream:

[tex]x - y =473.49\\[/tex] (in miles per hour)

Adding both the equations side by side, we get:

[tex]2x + y - y = 491.25 + 473.49\\\\x = \dfrac{964.74}{2} =482.37 \: \rm mph[/tex]

Using this value, we get the value of y as:

[tex]x + y =491.25\\y = 491.25 - x = 491.25 - 482.37 = 8.88 \: \rm mph[/tex]

Rounding to the nearest whole numbers, we get:

x = 482 mph, and y = 9 mph

Thus, the speed of the plane in still air is approx 482 miles per hour(mph). The speed of the jet stream, rounded to the nearest whole number, is 9 mph

Learn more about motion in stream here:

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