Question 149899
The Hudson River flows at a rate of 3 mile 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 x = speed of patrol boat in still water
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Time it takes to go up river:
60/(x-3)
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Time it takes to go down river:
60/(x+3)
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Therefore, we have:
60/(x-3) + 60/(x+3) = 9
multiplying both sides by (x-3)(x+3) we get:
60(x+3) + 60(x-3) = 9(x-3)(x+3)
60x + 180 + 60x - 180 = 9(x^2-9)
120x = 9x^2 - 81
0 = 9x^2 - 120X - 81
0 = 3x^2 - 40X - 27
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Since we can't factor, we must use the quadratic equation.  The solutions it gives is a positive and a negative answer.  Since it can't be negative we use the positive one.
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x = 14 mph
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Quadratic solution follows:
*[invoke quadratic "x", 3, -40, -27 ]