Question 160309
The speed of an airplane in still air is 243 mph. The plane travels 663 mi
 against the wind and 1735 mi with the wind in a total time of 10 hr.
 What is the speed of the wind?
:
Let x = speed of the wind
then
(243-x) = speed against the wind
and
(243+x) = speed with the wind
;
Write a time equation Time = {{{dist/speed}}}
:
{{{663/((243-x))}}} + {{{1735/((243+x))}}} = 10
:
Multiply equation by (243-x)(234+x); results:
663(243+x) + 1735(243-x) = 10(243-x)(243+x)
:
161109 + 663x + 421605 - 1735x = 10(59049 - x^2)
:
582714 - 1072x = 590490 - 10x^2
Arrange as a quadratic equation on the left:
+10x^2 - 1072x + 582714 - 590490 = 0
:
10x^2 - 1072x - 7776 = 0
:
Have to use the quadratic formula for this nasty equation
a=10; b= -1072; c=-7776
:
The positive solution x ~ 114 mph is the speed of the wind
:
:
Check solution by finding the total time:
663/(243-114) = 5.14 hr
1735/(243+114)= 4.86 hrs
--------------------------
total time   = 10.00 hrs