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 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) About Me  (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

60%2F%28r%2B30%29%2B60%2F%28r-30%29=13%2F10
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multiply both sides by 10%28r%2B30%29%28r-30%29;
600%28r-30%29%2B600%28r%2B30%29=13%28r%5E2-900%29
600r-18000%2B600r%2B1800=13r%5E2-13%2A900
1200r=13r%5E2-11700
highlight_green%2813r%5E2-1200r-11700=0%29
(discriminant, 569%2A60%5E2 )
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highlight_green%28r=%281200%2B60%2Asqrt%28569%29%29%2F26%29

highlight%28r=101.2%29

Answer by ikleyn(52852) 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.