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

Algebra ->  Radicals -> 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      Log On


   

Question 1102182: 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.
Answer by ikleyn(52775) About Me  (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

60%2F%28x%2B30%29 + 60%2F%28x-30%29 = 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  ====>


x%5B1%2C2%5D = %28120+%2B-+sqrt%28120%5E2+%2B+4%2A1.3%2A1.3%2A900%29%29%2F%282%2A1.3%29 = %28120+%2B-+143.12%29%2F2.6.


Only positive root makes sense  x = %28120+%2B+143.12%29%2F2.6 = 101.2.


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