SOLUTION: Orson rides his power boat up and down a canal. The water in the canal flows at 6 mph. Orson takes 5 hours longer to travel 360 miles against the current than he does to travel 360

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Question 985990: Orson rides his power boat up and down a canal. The water in the canal flows at 6 mph. Orson takes 5 hours longer to travel 360 miles against the current than he does to travel 360 miles with the current. What is the speed of Orson's boat in still water?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Orson rides his power boat up and down a canal.
The water in the canal flows at 6 mph.
Orson takes 5 hours longer to travel 360 miles against the current than he does to travel 360 miles with the current.
What is the speed of Orson's boat in still water?
:
let s = his speed in still water
then
(s-6) = his effective speed upstream
and
(s+6) = his effective speed downstream
:
Write a time equation, time = dist/speed
time up - time down = 5 hrs
360%2F%28%28s-6%29%29 - 360%2F%28%28s%2B6%29%29 = 5
multiply equation by (s-6)(s+6)
(s-6)(s+6)*360%2F%28%28s-6%29%29 - (s-6)(s+6)*360%2F%28%28s%2B6%29%29 = 5(s-6)(s+6)
Cancel the denominators, FOIL the right side
360(s+6) - 360(s-6) = 5(s^2 - 36)
:
360s + 2160 - 360s + 2160 = 5s^2 - 180
combine like terms
4320 + 180 = 5s^2
4500 = 5s^2
Simplify, divide both sides by 5
900 = s^2
s = sqrt%28900%29
s = 30 mph his speed in still water
:
:
see if this checks out, using the effective speeds
360%2F24 - 360%2F36 = 5
15 - 10 = 5 hrs