SOLUTION: a plane traveling 450 miles per hour can go 1000 miles with the wind in 1/2 hour less than when traveling against the wind. Find the speed of the wind.

Question 298137: a plane traveling 450 miles per hour can go 1000 miles with the wind in 1/2 hour less than when traveling against the wind. Find the speed of the wind.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a plane traveling 450 miles per hour can go 1000 miles with the wind in 1/2 hour
less than when traveling against the wind.
Find the speed of the wind.
:
Let w = speed of the wind
:
Plane effective ground speed:
(450+w) = with the wind
(450-w) = against the wind
:
Write a time equation, time = dist/speed:
:
Time against - time with = .5 hr
- = .5
:
Multiply by (450+w)(45-w), resulting in
1000(450+w) - 1000(450-w) = .5
:
450000 + 1000w - 450000+ 1000w = .5(450-w)(450+w)
:
2000w = .5(202500 - w^2)
:
2000w = 101250 - .5w^2
:
Arrange as a quadratic equation on the left
.5w^2 + 2000w - 101250 = 0
multiply by 1
w^2 + 4000w - 202500 = 0
Factor this to
(w+4050)(w-50) = 0
positive solution
w = 50 mph is the wind
;
:
Check solution by finding the times
1000/400 = 2.5
1000/500 = 2.0
--------------
differs by: .5 hr
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