SOLUTION: Cathy traveled by boat 4 miles upstream to fish. Because of the 5mph current it took her 40 minutes longer to get there than to return. How fast will her boat go in still water?

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Question 161270: Cathy traveled by boat 4 miles upstream to fish. Because of the 5mph current it took her 40 minutes longer to get there than to return. How fast will her boat go in still water?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Cathy traveled by boat 4 miles upstream to fish. Because of the 5mph current it took her 40 minutes longer to get there than to return. How fast will her boat go in still water?
:
Let s = speed in still water
then
(s+5) = speed downstream
and
(x-5) = speed upstream
:
Change 40 min to hrs: 40 min = 2%2F3 hr
:
Write time equation; time = dist%2Fspeed
:
Downstream time + 2/3 hr = upstream time
4%2F%28%28s%2B5%29%29 + 2%2F3 = 4%2F%28%28s-5%29%29
:
Multiply equation by 3(s-5)(s+5) to get rid of the denominators
:
4(3(s-5)) + 2(s-5)(s+5) = 4(3(s+5))
:
12s - 60 + 2(s^2 - 25) = 12s + 60
:
12s - 60 + 2s^2 - 50 = 12s + 60
Combine like terms on the left
2s^2 + 12s - 12s - 60 - 50 - 60 = 0
:
2s^2 - 170 = 0
:
2s^2 = +170
s^2 = 170%2F2
s^2 = 85
s = sqrt%2885%29
s = 9.22 mph in still water
:
:
Check solution on a calc:
4/14.22 + .67 = .95
4/4.22 = .95