SOLUTION: A speedboat takes 4 hours longer to go 80 miles up a river than to return. If the boat cruises at 15 miles per hour in still water, what is the rate of the current?

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Question 387782: A speedboat takes 4 hours longer to go 80 miles up a river than to return. If the boat cruises at 15 miles per hour in still water, what is the rate of the current?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
R%2At=D
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Let the current speed be C.
With the current,
%2815%2BC%29%2At=80
t=80%2F%2815%2BC%29
Against the current,
%2815-C%29%2A%28t%2B4%29=80
t%2B4=80%2F%2815-C%29
Subsituting,
80%2F%2815%2BC%29%2B4=80%2F%2815-C%29
Use the common denominator, %2815-C%29%2815%2BC%29

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%2880%2815-C%29%2B4%2815-C%29%2815%2BC%29-80%2815%2BC%29%29%2F%28%2815-C%29%2815%2BC%29%29=0
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%281200-80C%2B900-4C%5E2-1200-80C%29%2F%28%2815-C%29%2815%2BC%29%29=0
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%28900-160C-4C%5E2%29%2F%28%2815-C%29%2815%2BC%29%29=0
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%28225-40C-C%5E2%29%2F%28%2815-C%29%2815%2BC%29%29=0
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%28%285-C%29%2845%2BC%29%29%2F%28%2815-C%29%2815%2BC%29%29=0
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Only one solution since C%3E=0
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highlight%28C=5%29mph