SOLUTION: I do not understant how to set up a rational equation for word probles such as this. Debbie traveled by boat 5 miles upstream to fish. Because of the 4 mph current, it took her 40

Question 757381: I do not understant how to set up a rational equation for word probles such as this.
Debbie traveled by boat 5 miles upstream to fish. Because of the 4 mph current, it took her 40 minutes longer to get there than to return. How fast will her boat go in still water?
Could you please help me, thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Debbie traveled by boat 5 miles upstream to fish. Because of the 4 mph current, it took her 40 minutes longer to get there than to return. How fast will her boat go in still water?
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Upstream DATA: distance = 5 miles ; rate = b-4 mph ; time = d/r = 5/(b-4)
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Downstream DATA: distance = 5 miles ; b+4 mph ; time = d/r = 5/(b+4)
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Equation:
up time - down time = 2/3 hrs.
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5/(b-4) - 5/(b+4) = 2/3
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Multiply thru by 3(b-4)(b+4) to get:
15(b+4) - 15(b-4) = 2(b^2-16)
60 + 60 = 2b^2-32
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60 = b^2 - 16
b^2 = 76
Positive solution:
b = 8.72 mph (speed of the boat in still water)
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Cheers,
Stan H.
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