SOLUTION: A pilot flew his​ single-engine airplane 90 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 1102559: A pilot flew his​ single-engine airplane 90 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 20 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 ikleyn, josgarithmetic:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A pilot flew his​ single-engine airplane 90 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 20 miles per​ hour, and the total time
going and returning was 1.3 hours, find the speed of the plane in still air.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

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.

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

90*(x+20) + 90*(x-20) = 1.3*(x^2-400)  ====>


180x = 1.3x^2 - 1.3*400  ====>  1.3x^2 - 180x - 1.3*400 = 0  ====>


 =  = .


Only positive root makes sense  x =  = 141.29.


Answer.  The speed of the plane "at no wind" is 141.29 miles per hour.



Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
                     SPEED       TIME           DISTANCE
GOING                r+20        90/(r+20)       90
RETURN               r-20        90/(r-20)       90
TOTAL                            1.3            180

Solve this for r.
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