SOLUTION: Debbie traveled by Boat 5 miles upstream to fish. Because of the 4mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water

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Question 222063: Debbie traveled by Boat 5 miles upstream to fish. Because of the 4mph current, it took her 20 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!
Debbie traveled by boat 5 miles upstream to fish.
Because of the 4 mph current, it took her 20 minutes longer to get there
than to return.
How fast will her boat go in still water?
:
Let s = boat speed in still water
then
(s-4) = speed upstream
and
(s+4) = speed down stream
:
Convert 20 min to hrs: 20/60 = 1%2F3hr
:
Write a time equation: time = distance%2Fspeed
Upstream time = downstream time + 20 minutes (1/3 hr)
5%2F%28%28s-4%29%29 = 5%2F%28%28s%2B4%29%29 + 1%2F3
:
To clear out these denominators, multiply equation by 3(s+4)(s-4)
3(s+4)(s-4)*5%2F%28%28s-4%29%29 = 3(s+4)(s-4)*5%2F%28%28s%2B4%29%29 + 1%2F3*3(s+4)(s-4)
Results in
:
15(s+4) = 15(s-4) + (s+4)(s-4)
:
15s + 60 = 15s - 60 + s^2 - 16
:
0 = 15s - 15s - 60 - 60 + s^2 - 16
:
0 = s^2 - 136
:
s^2 = 136
s = sqrt%28136%29
s = 11.66 mph speed in still water
:
:
Check solution on calc: (speed up = 7.66 and speed down = 15.66)
5/7.66 - 5/15.66 = .3333 which is 1/3 of an hr