SOLUTION: Please help me translate this into a quadratic equation and solve. The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Please help me translate this into a quadratic equation and solve. The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in      Log On


   

Question 139175: Please help me translate this into a quadratic equation and solve.
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 ankor@dixie-net.com(22740) About Me  (Show Source):
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he 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 s = speed of the boat in still water
:
(s-3) = speed upstream
(s+3) = speed downstream
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Write a time equation; Time = dist/speed
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Time upstream + time downstream = 9 hr
60%2F%28%28s-3%29%29 + 60%2F%28%28s%2B3%29%29 = 9
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multiply equation by (s-3)(s+3) to get rid of the denominators:
(s-3)(s+3)*60%2F%28%28s-3%29%29 + (s-3)(s+3)*60%2F%28%28s%2B3%29%29 = 9(s-3)(s+3)
:
60(s+3) + 60(s-3) = 9(s^2 - 9)
:
60s + 180 + 60s - 180 = 9s^2 - 81
:
120s = 9s^2 - 81
:
0 = 9s^2 - 120s - 81
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Simplify, divide equation by 3, giving us a simple quadratic equation
3s^2 - 40s - 27 = 0
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We need to use the quadratic formula to solve for s: a=3; b=-40; c=-27
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The positive solution = 13.977 ~ 14 mph
:
:
Check solution using 14 mph
60/17 + 60/11 =
3.529 + 5.454 = 8.983 ~ 9 hrs