SOLUTION: In still water a tugboat can travel 15 miles per hour. It travels 36 miles upstream and then 36 miles downstream in a total time of 5 hours. Find the speed of the current.

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Question 319437: In still water a tugboat can travel 15 miles per hour. It travels 36 miles upstream and then 36 miles downstream in a total time of 5 hours. Find the speed of the current.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let c = speed of current
15+-+c = speed going upstream
15+%2B+c = speed going downstream
(1)36+=+%2815+-+c%29%2At%5Bu%5D
(2) 36+=+%2815+%2B+c%29%2At%5Bd%5D
(3) t%5Bu%5D+%2B+t%5Bd%5D+=+5
----------------------------
(1)36+=+%2815+-+c%29%2At%5Bu%5D
t%5Bu%5D+=+36%2F%2815+-+c%29
and
(2) 36+=+%2815+%2B+c%29%2At%5Bd%5D
t%5Bd%5D+=+36%2F%2815+%2B+c%29
Adding:
t%5Bu%5D+%2B+t%5Bd%5D+=+36%2A%281%2F%2815+-+c%29+%2B+1%2F%2815+%2B+c%29%29
5+=+36%2A%281%2F%2815+-+c%29+%2B+1%2F%2815+%2B+c%29%29
Multiply both sides by %2815+-+c%29%2815+%2B+c%29
5%2A%28225+-+c%5E2%29+=+36%2A%2815+%2B+c+%2B+15+-+c%29
1125+-+5c%5E2+=+36%2A30
5c%5E2+=+1125+-+1080
5c%5E2+=+45
c%5E2+=+9
c+=+3
The current is 3 mi/hr
check:
t%5Bu%5D+%2B+t%5Bd%5D+=+36%2A%281%2F%2815+-+c%29+%2B+1%2F%2815+%2B+c%29%29
t%5Bu%5D+%2B+t%5Bd%5D+=+36%2A%281%2F%2815+-+3%29+%2B+1%2F%2815+%2B+3%29%29
t%5Bu%5D+%2B+t%5Bd%5D+=+36%2A%281%2F12+%2B+1%2F18%29
t%5Bu%5D+%2B+t%5Bd%5D+=+36%2F12+%2B+36%2F18
t%5Bu%5D+%2B+t%5Bd%5D+=+3+%2B+2
OK