SOLUTION: The excursion boat on the river takes 2� hours to make the trip to a point 12 miles upstream and to return. If the rate at which the boat travels in still water is 5 times the rate

Question 192908: The excursion boat on the river takes 2� hours to make the trip to a point 12 miles upstream and to return. If the rate at which the boat travels in still water is 5 times the rate of the river current, what is the rate of the current?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The excursion boat on the river takes 2� hours to make the trip to a point 12 miles upstream and to return. If the rate at which the boat travels in still water is 5 times the rate of the river current, what is the rate of the current?
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Let the current speed be "c";
Then the boat speed in still wate is "5c":
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Upstream speed:
distance = 12 miles ; rate = 5c-c = 4c mph ; time = 12/4c = 3/c hrs
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Downstream speed:
distance = 12 miles ; rate = 5c+c = 6c mph ; time = 12/6c = 2/c hrs
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Equation:
time + time = 2 1/2 hrs
3/c + 2/c = 5/2
Multiply thru by 2c to get:
6 + 4 = 5c
c = 2 mph (speed of the current)
5c = 10 mph (speed of the boat in still water)
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Cheers,
Stan H.
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