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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
(s+5) = boat speed down-stream
(s-5) = boat speed up-stream
Write a time equation; Time =
Upstream time + downstream time = 6 hrs
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
(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?