Catherine is camping along a river It takes her 15 hours to

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 rivers current and the rate of Catherines paddeling in still water?

Solution

Upstream DATA:
distance = 6 miles: time = 1.5 hours: rate = 6/(3/2) = 4 mph
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Downstream DATA:
distance + 6 miles ; time = 1 hr ; rate = 6/1 = 6 mph
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Equations:
b - c = 4 mph
b + c = 6 mph
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2b = 10
b = 5 mph (speed of the boat in still water)
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Substitute to solve for \"c\":
5 - c = 4
c = 1 mph (speed of the currect)