SOLUTION: A motor boat travels 30 miles up a river and returned a distance of 27 miles. The entire trip takes 5 hours. If the rate of the motor in still water is 12 mph, find the rate of the

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Question 535144: A motor boat travels 30 miles up a river and returned a distance of 27 miles. The entire trip takes 5 hours. If the rate of the motor in still water is 12 mph, find the rate of the current of the river.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A motor boat travels 30 miles up a river and returned a distance of 27 miles. The entire trip takes 5 hours.
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If the rate of the motor in still water is 12 mph,
Upstream DATA:
distance = 30 miles ; rate = 12-c mph ; time = 30/(12-c) hrs
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Downstream DATA:
distance = 27 miles ; rate = 12+c mph ; time = 27/(12+c) hrs
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Find the rate of the current of the river.
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Equation:
time + time = 5 hrs.
30/(12-c) + 27/(12+c) = 5
30(12+c) + 27(12-c) = 5(144-c^2)
360 + 30c + 324 - 27c = 720 - 5c^2
5c^2 +3c -36 = 0
Positive solution:
x = 2.4 mph (speed of the current)
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Cheers,
Stan H.
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