SOLUTION: The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water?

Question 154736This question is from textbook
: The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water? This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The Hudson River flows at a rate of 3 miles per hour.
A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water?
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Let the boat speed be "b".
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Upstream DATA:
distance = 60 miles ; rate = b-3 ; time = 60/(b-3) hrs.
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Downstream DATA:
distance = 60 miles ; rate = b+3 ; time = 60/(b+3) hrs
---------------------
EQUATION:
time up + time down = 9 hrs
60/(b-3) + 60/(b+3) = 9
60b + 180 + 60b - 180 = 9(b^2-9)
120b = 9b^2 - 81
9b^2 -120b - 81 = 0
b = -0.643904; b = 13.977237...
Positive solution:
boat speed = 13.977237..
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Cheers,
Stan H.

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