SOLUTION: plane flies 420 mph in still air. With wind, a trip from a to b takes 10 minutes less than the return trip flying against wind from b to a. Distance between a to b is 360 miles. Fi

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Question 220972: plane flies 420 mph in still air. With wind, a trip from a to b takes 10 minutes less than the return trip flying against wind from b to a. Distance between a to b is 360 miles. Find speed of wind.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
plane flies 420 mph in still air. With wind, a trip from a to b takes 10 minutes
less than the return trip flying against wind from b to a.
Distance between a to b is 360 miles.
Find speed of wind.
:
Let w = speed of the wind
then
(420+w) = speed with the wind
and
(420-w) = speed against the wind
:
Convert 10 min to 1%2F6 hr
:
Time b-a - Time a-b = 10 min
360%2F%28%28420-w%29%29 - 360%2F%28%28420%2Bw%29%29 = 1%2F6
Multiply equation by 6(420-w)(420+w)
:
6(420-w)(420+w)*360%2F%28%28420-w%29%29 - 6(420-w)(420+w)*360%2F%28%28420%2Bw%29%29 = 6(420-w)(420+w)*1%2F6
:
Cancel the denominators and you have
6(420+w)*360 - 6(420-w)*360 = (420+w)(420-w)
;
2160(420+w) - 2160(420-w) = 176400 - w^2
:
1327200 + 2160w - 1327200 + 2150w = 176400 - w^2
:
Combine on the left to form a quadratic equation:
w^2 + 4320w - 176400 = 0
You have to use the quadratic formula to find w
:
I got a positive solution of w = 40.4545 mph
;
:
Check this with a calc
360%2F%28%28420-40.4545%29%29 - 360%2F%28%28420%2B40.4545%29%29 = 1%2F6
.9485 - .7818 = .1667
.1667 = .1667