SOLUTION: A kayaker travels downstream 15 miles and then travels back upstream to a point which is 1 mile short of where he originally departed from. The entire trip takes 3 hours. in still
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Question 900400: A kayaker travels downstream 15 miles and then travels back upstream to a point which is 1 mile short of where he originally departed from. The entire trip takes 3 hours. in still water the kayaker paddles at a rate of 10 miles per hour. how fast is the current of the stream?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A kayaker travels downstream 15 miles and then travels back upstream to a point which is 1 mile short of where he originally departed from. The entire trip takes 3 hours. in still water the kayaker paddles at a rate of 10 miles per hour. how fast is the current of the stream?
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Downstream DATA:
distance = 15 miles ; rate = 10+c mph ; time = d/r = 15/(10+c) hrs
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Upstream DATA:
distance = 14 miles ; rate = 10-c mph ; time = d/r = 14/(10-c) hrs
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Equation:
time + time = 3 hrs.
15/(10+c) + 14/(10-c) = 3 hrs
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15*(10-c) + 14(10+c) = 3(100-c^2)
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150-15c + 140+14c = 300 - 3c^2
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290 - c = 300 - 3c^2
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3c^2 -c -10 = 0
3c^2 -6c + 5c -10 = 0
3c(c-2) + 5(c -2) = 0
(c-2)(3c+5) = 0
Positive solution:: c = 2 mph (speed of the current)
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Cheers,
Stan H.
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