SOLUTION: This is a strange problem our instructor gave us to solve. I cannot figure out how to do this particular probem. Can someone please help? Here it is. The Ohio River flows at a

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Question 187033: This is a strange problem our instructor gave us to solve. I cannot figure out how to do this particular probem. Can someone please help? Here it is. The Ohio River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver and returns in a total of 6 hours. What is the speed of the boat in still water? I am so confused...
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The Ohio River flows at a rate of 5 miles per hour.
A patrol boat travels 40 miles upriver and returns in a total of 6 hours.
What is the speed of the boat in still water?
:
Let s = boat speed in still water
then
(s+5) = boat speed down-stream
and
(s-5) = boat speed up-stream
:
Write a time equation; Time = dist%2Fspeed
;
Upstream time + downstream time = 6 hrs
40%2F%28%28s-5%29%29 + 40%2F%28%28s%2B5%29%29 = 6
:
Multiply equation by (s-5)(s+5) and you have:
40(s+5) + 40(s-5) = 6(s+5)(s-5)
:
40s + 200 + 40s - 200 = 6(s^2 - 25)
:
80s = 6s^2 - 150
:
0 = 6s^2 - 80s - 150; a quadratic equation
Simplify, divide by 2
3s^2 - 40s - 75 = 0
Factors to:
(3s + 5) (s - 15) = 0
The positive solution is what we want
s = 15 mph is the speed in still water
;
;
Check solution in our original equation
40/20 = 2 hr
40/10 = 4 hr
;
:
Did this reduce the confusion somewhat? Any questions?