Question 161585
A river is flowing at a rate of 5 km/h. A boat travels 12km upstream and 36km downstream in a total of 9hours. What is the speed of the boat in still water?
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B = speed of boat
B-5 = speed of boat upstream
B+5 = speed downstream
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h = hours going upstream
h*(B-5) = 12
(9-h)*(B+5) = 36
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B = 12/h + 5
B = 36/(9-h) - 5
B = 12/h + 5 = 36/(9-h) - 5
12/h + 10 = 36/(9-h)
Multiply by h*(9-h)
12(9-h) + 10h(9-h) = 36h
108-12h + 90h-10h^2 = 36h
Collect terms
-10h^2 + 42h + 108 = 0
5h^2 - 21h - 54 = 0
*[invoke solve_quadratic_equation 5,-21,-54]
The online solver always uses x, so sub h for x.
The -1.8 hours is not usable, so the time going upstream is,
h = 6 hours.
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Sub h into B = 12/h + 5 to solve for B
B = 12/6 + 5
B = 7 kph
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The people should have gotten out and walked, woulda been faster.