SOLUTION: A pilot flew his​ single-engine airplane 60 miles with the wind from City A to above City B. He then turned around and flew back to City A against the wind. If the wind was a

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Question 1102184: A pilot flew his​ single-engine airplane 60 miles with the wind from City A to above City B. He then turned around and flew back to City A against the wind. If the wind was a constant 30 miles per​ hour, and the total time going and returning was 1.3 hours, find the speed of the plane in still air.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
                 SPEED      TIME          DISTANCE

WWIND            r+30       60/(r+30)     60

AGNSTWIND        r-30       60/(r-30)     60

TOTAL                         1.3


-
multiply both sides by ;




(discriminant, )
-



Answer by ikleyn(52855)   (Show Source): You can put this solution on YOUR website!
.
Let x be the speed of plane at no wind", in miles per hour (mph).

Then the speed with the wind is (x+30) mph,
     the speed against the wind is (x-30) mph.


Then the "time equation" is

 +  = 1.3   hours.

======================================>

60*(x+30) + 60*(x-30) = 1.3*(x^2-900)  ====>


120x = 1.3x^2 - 1.3*900  ====>  1.3x^2 - 120x - 1.3*900 = 0  ====>


 =  = .


Only positive root makes sense  x =  = 101.2.


Answer.  The speed of the plane "at no wind" is 101.2 miles per hour.


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