Question 180015: Catherine is camping along a river. It takes her 1.5 hours to paddle her canoe 6 miles upstream from her campsite. Catherine turns her canoe around and returns 6 miles downstream to her campsite in exactly 1 hour. What is the rate of the river's current and the rate of Catherine's paddling in still water?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Catherine is camping along a river. It takes her 1.5 hours to paddle her canoe
6 miles upstream from her campsite. Catherine turns her canoe around and
returns 6 miles downstream to her campsite in exactly 1 hour.
:
What is the rate of the river's current and the rate of Catherine's paddling in still water?
:
Let s = paddling speed in still water
Let c = river current speed
Then we can say:
(s+c) = speed downstream
(s-c) = speed upstream
:
Write a distance equation for each half of the round trip, dist = time * speed:
;
1.5(s-c) = 6; upstream
1.0(s+c) = 6; downstream
:
you can simplify the 1st equation, divide both sides by 1.5 and you have:
s - c = 4
s + c = 6
-------------addition eliminates c, find s:
2s = 10
s = 5 mph paddling in still water
:
Find c using s + c = 6
5 + c = 6
c = 6 - 5
c = 1 mph is the current
:
Check solution in the 1st equation
1.5(5 - 1) =
1.5 * 4 = 6; confirms our solutions
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