SOLUTION: Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 6-mph current, it took her 40 minutes longer to get there than to return. How fast will her bo

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Question 545564: Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 6-mph current, it took her 40 minutes longer to get there than to return. How fast will her boat go in still water? (Please round your answer to one decimal place.)
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 in her favorite spot.
Because of the 6 mph current, it took her 40 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-6) = speed upstream
and
(s+6) = speed down stream
:
Convert 40 min to hrs: 40/60 = 2%2F3hr
:
Write a time equation: time = distance%2Fspeed

Upstream time = downstream time + 40 minutes (2/3 hr)
5%2F%28%28s-6%29%29 = 5%2F%28%28s%2B6%29%29 + 2%2F3
:
To clear out these denominators, multiply equation by 3(s+6)(s-6)
3(s+6)(s-6)*5%2F%28%28s-6%29%29 = 3(s+6(s-6)*5%2F%28%28s%2B6%29%29 + 2%2F3*3(s+6)(s-6)
Results in
:
15(s+6) = 15(s-6) + 2(s+6)(s-6)
:
15s + 90 = 15s - 90 + 2(s^2 - 36)
:
15s + 90 = 15s - 90 + 2s^2 - 72
:
0 = 15s - 15s - 90 - 90 + 2s^2 - 72
:
2s^2 - 252 = 0
:
2s^2 = 252
Divide by 2
s^2 = 126
s = sqrt%28126%29
s = 11.225 mph speed in still water
:
:
Check solution on calc: (speed up = 5.225 and speed down = 17.225)
5/5.225 - 5/17.225 = .6667 which is 2/3 of an hr