SOLUTION: 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 Ca

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
.
1.5*(p-c) = 6 miles = distance upstream
1*(p+c) = 6 miles = distance downstream
.
multiplying through
.
1.5p - 1.5c = 6
p + c = 6
.
dividing the first equation by 1.5
p - c = 4
.
solving as simultaneous equation, we can add them
p + c = 6
p - c = 4
2p = 10
p = 5 = paddling rate
.
substituting this value
p + c = 6
5 + c = 6
c = 1
.
checking by substituting in the other equation
.
1.5(p-c) = 6 ??
1.5(5-1) = 1.5*4 = 6
yes
.
so the answer is:
The rate of the current is 1 mph.
Cathy's paddling rate in still water is 5 mph.
.
done
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