SOLUTION: 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?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 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?      Log On


   

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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Fspeed
:
663%2F%28%28243-x%29%29 + 1735%2F%28%28243%2Bx%29%29 = 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