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please explain how to set up this word problem

Algebra
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The excursion boat on the river takes 2 1/2 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?

Oct 22nd, 2014

As I understand from the problem that the givens are for the boat in still water, and I will solve it accordingly.

Rate = change/unit time, for this problem since the distance changes and time is in hours, 

the rate = distance in miles/ hour

Total distance traveled by the boat = 12 * 2 = 24 miles. (upstream and back)

So, the boat travels 24 miles   in   2 1/2 hours

                                  ? miles     in     1 hour

The rate at which the boat travels =  24 * 1 / 2.5 = 9.6 miles/hour

Assume the rate of current = x,   then the rate of travel in still water = 5x 

Therefore, 5x = 9.6 

                  x = 9.6/5 = 1.92 miles/hour

This means that current moves 1.92 miles each hour. (the river's velocity)

Oct 22nd, 2014

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Oct 22nd, 2014
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