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.
:
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 = {{{dist/speed}}}

Against wind time + With wind time = 11 hr
{{{689/((168-x))}}} + {{{950/((168+x))}}} = 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