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 153972: 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?

Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
distance=rate*time
d=rt
d/r=t
60/(r-3)+60/(r+3)=9
[60(r+3)+60(r-3)]/(r-3)(r+3)=9
60r+180+60r-180=9(r-3)(r+3)
120r=9(r^2-9)
120r=9r^2-81
9r^2-120r-81=0

r=(120+-sqrt[-120^2-4*9*-81])/2*9
r=(120+-sqrt[14,400+2,916])/18
r=(120+-sqrt17,316)/18
r=(120+-131.59)/18
r=(120+131.59)/18
r=251.59/18
r=13.98 mph for the speed of the boat.
proof:
60/(13.98-3)+60/13.98+3)=9
60/10.98+60/16.98=9
5.4645+3.5335=9
9~9

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