SOLUTION: The speed of an airplane in still air is 168 mph. The plane travels 689 miles against the wind and 950 miles with the wind in a total time of 11 hours. What is the speed of the win

Question 160814: The speed of an airplane in still air is 168 mph. The plane travels 689 miles against the wind and 950 miles with the wind in a total time of 11 hours. What is the speed of the wind.
I have tried everything with this question and I keep getting the wrong answer. I think I am screwing up distributing.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The speed of an airplane in still air is 168 mph. The plane travels 689 miles
against the wind and 950 miles with the wind in a total time of 11 hours.
What is the speed of the wind.
:
Let x = speed of the wind
then
(168-x) = speed against the wind
and
(168+x) = speed with the wind
:
Write a time equation: Time =
Against wind time + With wind time = 11 hr
+ = 11
:
Multiply equation by (168+x)(168-x), results:
689(168+x) + 950(168-x) = 11(168+x)(168-x)
:
115752 + 689x + 159600 - 950x = 11(28224 - x^2)
:
-261x + 275352 = 310464 - 11x^2
:
Arrange as quadratic equation on the left
+11x^2 - 261x + 275352 - 310464 = 0
:
11x^2 - 261x - 35112 = 0
:
This nasty equation requires the quadratic formula; a=11; b=-261; c=-35112
You should get positive solution: x ~ 69.6 mph speed of the wind
:
:
We can confirm that:
689/(268-69.6) = 7.00 hrs
950/(268+69.6) = 4.00 hrs
---------------------------
total time = 11 hrs
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