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?

Question 387781: 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 robertb(5830) (Show Source): You can put this solution on YOUR website!
Let c = rate of the current.
Then 15+c = rate of speedboat down the river
15 - c = rate of speedboat up the river
From the Formula D = R*T, we get T = D/R, so
= time of speedboat up the river
= time of speedboat down the river. From these we get
, or .
Combining and simplifying, we get
, or , or (c-5)(c+45) = 0.
Hence c = 5 miles per hour, the rate of the current.
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