Question 1102559
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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.
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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

{{{90/(x+20)}}} + {{{90/(x-20)}}} = 1.3   hours.

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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  ====>


{{{x[1,2]}}} = {{{(120 +- sqrt(180^2 + 4*1.3*1.3*400))/(2*1.3)}}} = {{{(180 +- 187.36)/2.6}}}.


Only positive root makes sense  x = {{{(180 + 187.36)/2.6}}} = 141.29.


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