The excursion boat on the river takes 2½ 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?

2 mph

Step-by-step explanation:

time = distance / speed

Let c represent the rate of the current. Then the upstream rate of the boat relative to the shore is (5c -c) = 4c, and the upstream time is ...

... 12/(4c) = 3/c.

Likewise, the downstream rate is (5c +c) = 6c, and the downstream time is ...

... 12/(6c) = 2/c.

The total time is the sum of upstream and downstream times:

... 3/c +2/c = 2.5

... 5/c = 2.5 . . . . . . combine terms

... 5/2.5 = c = 2 . . . multiply by c/2.5

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