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

Algebra ->  Equations -> 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      Log On


   

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(52777) About Me  (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

90%2F%28x%2B20%29 + 90%2F%28x-20%29 = 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  ====>


x%5B1%2C2%5D = %28120+%2B-+sqrt%28180%5E2+%2B+4%2A1.3%2A1.3%2A400%29%29%2F%282%2A1.3%29 = %28180+%2B-+187.36%29%2F2.6.


Only positive root makes sense  x = %28180+%2B+187.36%29%2F2.6 = 141.29.


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



Answer by josgarithmetic(39617) About Me  (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.
90%2F%28r%2B20%29%2B90%2F%28r-20%29=1.3