Question 1102182
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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

{{{60/(x+30)}}} + {{{60/(x-30)}}} = 1.3   hours.

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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  ====>


{{{x[1,2]}}} = {{{(120 +- sqrt(120^2 + 4*1.3*1.3*900))/(2*1.3)}}} = {{{(120 +- 143.12)/2.6}}}.


Only positive root makes sense  x = {{{(120 + 143.12)/2.6}}} = 101.2.


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