Question 1200756
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A plane can travel 1,015 miles in 7 hours traveling against the wind. 
Traveling with the same wind, the plane can travel 820 miles in 4 hours. 
How fast can the plane travel in still air and how fast is the wind current?
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<pre>
Let u be the plane speed in still air,
and let v be the rate of the wind.


The effective speed of the plane with the wind is

    u + v = {{{820/4}}} = 205 miles per hour.    (1)


The effective speed of the plane against the wind is

    u - v = {{{1015/7}}} = 145 miles per hour.    (2)


Add equations (1) and (2) and find u

    2u = 205 + 145 = 350,  u = 350/2 = 175 miles per hour (the speed of the plane in still air).


From equation (1), find v

    v = 205 - 175 = 30 miles per hour (the rate of the wind).


<U>ANSWER</U>.  The speed of the plane in still air is 175 miles per hour.

         The rate of the wind is 30 miles per hour.
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Solved.