SOLUTION: Please help me solve this problem. A person paddles 1 mi upstream and 1 mile down stream in a total of 1 hour. The speed of the river is 2mph. What is the speed of the persons b

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Question 868686: Please help me solve this problem.
A person paddles 1 mi upstream and 1 mile down stream in a total of 1 hour. The speed of the river is 2mph. What is the speed of the persons boat in still water?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this problem.
A person paddles 1 mi upstream and 1 mile down stream in a total of 1 hour. The speed of the river is 2mph. What is the speed of the persons boat in still water?
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Let "b" be the speed of the boat in still water.
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Upstream DATA:
distance = 1 mile ; rate = b-2 mph ; time = d/r = 1/(b-2) hrs
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Downstream DATA:
distance = 1 mile ; rate = b+2 mph ; time = d/r = 1/(b+2) hrs
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Equation:
time + time = 1 hr.
1/(b-2) + 1/(b+2) = 1
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b+2 + b-2 = b^2-4
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2b = b^2-4
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b^2-2b-4 = 0
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Use the quadratic formula to get:
b = [2 +- sqrt(4-4*-4)]/2
b = [2 +- sqrt(20)]/2
Positive solution::
b = [2+2sqrt(5)]/2
b = 1+sqrt(5)
b = 3.24 mph (speed of the boat in stil water)
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Cheers,
Stan H.
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