<PRE><B>Question 80784</B>
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 speed of the boat in still water be &quot;b&quot;
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Upriver DATA:
distance = 60 mi ; rate = b-3 mph ; time = d/r = 60/(b-3) hrs.
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Downriver DATA:
distance = 60 mi; rate = b+3 ; time = d/r = 60/(b+3) hrs.
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EQUATION:
time up + time down = 9 hrs
60/(b-3) + 60/(b+3) = 9
Divide thru by 60 to get:
1/(b-3) + 1/(b+3) = 3/20
Multiply thru by 20(b-3)(b+3) to get:
20(b+3) + 20(b-3) = 3(b^2-9)
40b=3b^2-27
3b^2-40b-27=0
b=[40+-sqrt(40^2-4*3*-27)]/6
b=[40+-2sqrt(491)]/6
Positive Answer: b=14.0528 mph (this is the speed of the boat in still water)
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Cheers,
Stan H. 

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