SOLUTION: I am a home schooled student and i do not have a text book curriculum. The excursion boat on a river takes 2 1/2 hours to make the trip to a point 12 miles upstream and to return.

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Question 36973: I am a home schooled student and i do not have a text book curriculum.
The excursion boat on a river takes 2 1/2 hours to make the trip to a point 12 miles upstream and to return. If the rate at whick the boat travels in still water is 5 times the rate of the river current, what is the rate of the current?

Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Leeting x be the rate fo the current:
2 1/2 hours ->2.5 hours
Equation:
12%2F%285x%2Bx%29%2B12%2F%285x-x%29=2.5
12[(6x)+(4x)]=2.5[(6x)(4x)]
12%2810x%29=2.5%2824x%5E2%29
120x=60x%5E2
x%5E2-2x=0
x(x-2) or...
d0%2Fdt=2x%28dx%2Fdt%29-2%28dx%2Fdt%29
x=1
Multiply the result by 2
x=2
Hence, the rate of the current is 2mph.
Paul.