Question 139175
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
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(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/((s-3))}}} + {{{60/((s+3))}}} = 9
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multiply equation by (s-3)(s+3) to get rid of the denominators:
(s-3)(s+3)*{{{60/((s-3))}}} + (s-3)(s+3)*{{{60/((s+3))}}} = 9(s-3)(s+3)
:
60(s+3) + 60(s-3) = 9(s^2 - 9)
:
60s + 180 + 60s - 180 = 9s^2 - 81
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120s = 9s^2 - 81
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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
:
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Check solution using 14 mph
60/17 + 60/11 =
3.529 + 5.454 = 8.983 ~ 9 hrs