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Question 277280: It takes Cathy 1.5 hours to paddle her canoe 6 miles upstream. Then she turns her canoe around and paddles 6 miles downstream in 1 hour. What is the rate of the current? What is Cathy's paddling rate in still water?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! p = paddling rate in still water
c = current flow
p-c = speed going upstream
p+c = speed going downstream
d = rt, where d=distance, r=rate (or speed), and t= time
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1.5*(p-c) = 6 miles = distance upstream
1*(p+c) = 6 miles = distance downstream
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multiplying through
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1.5p - 1.5c = 6
p + c = 6
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dividing the first equation by 1.5
p - c = 4
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solving as simultaneous equation, we can add them
p + c = 6
p - c = 4
2p = 10
p = 5 = paddling rate
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substituting this value
p + c = 6
5 + c = 6
c = 1
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checking by substituting in the other equation
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1.5(p-c) = 6 ??
1.5(5-1) = 1.5*4 = 6
yes
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so the answer is:
The rate of the current is 1 mph.
Cathy's paddling rate in still water is 5 mph.
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done
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