SOLUTION: A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. Find the speed the kayaker would make in still water.

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Question 66568: A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. Find the speed the kayaker would make in still water.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. Find the speed the kayaker would make in still water
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Let the speed of the boat in calm water be "b".
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Down river DATA:
Distance = x miles ; Time = 2 hrs ; Rate = x/2 mph
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Up river DATA:
Distance = x miles; time = 3 hrs ; Rate = x/3
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EQUATIONS:
b+6=x/2
b-6=x/3
Subtract one from the other:
12=(x/2)-(x/3)
Multiply thru by 6 to get:
72= 3x-2x
x=72 miles (distance down the river)
Solve one of the equations for b as follows:
b+6=(72/2)
b+6=36
b=30 mph (speed of the boat in still water)
Cheers,
Stan H.