SOLUTION: Bill can row 3 mph in still water. It takes him 3 hours 36 minutes to go 3 miles upstream and return. Find the speed of the current. I know this problem is d=rt kind of problem

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Question 1108948: Bill can row 3 mph in still water. It takes him 3 hours 36 minutes to go 3 miles upstream and return. Find the speed of the current.
I know this problem is d=rt kind of problem. I did the math and the answer that I came up with 3 mph. Which now thinking about it doesn't sound right.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the speed of the current in mi/hr
Let +t+ = time in hrs to go upstream
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Convert +36+ min to hrs:
+36%2F60+=+.6+
+3.6+ hrs = total times for both trips
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Equation for going upstream:
(1) +3+=+%28+3+-+c+%29%2At+
Equation for going downstream:
(2) +3+=+%28+3+%2B+c+%29%2A%28+3.6+-+t+%29+
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(2) +3+=+10.8+%2B+3.6c+-+t%2A%28+3+%2B+c+%29+
(2) +t%2A%28+3+%2B+c+%29+=+7.8+%2B+3.6c+
and
(1) +t+=+3%2F%28+3+-+c+%29+
and
(2) +%28+3%2F%28+3+-+c+%29+%29%2A%28+3+%2B+c+%29+=+7.8+%2B+3.6c+
(2) +3%2A%28+3+%2B+c+%29+=+%28+7.8+%2B+3.6c+%29%2A%28+3+-+c+%29+
(2) +9+%2B+3c+=+23.4+%2B+10.8c+-+7.8c+-+3.6c%5E2+
(2) +3.6c%5E2+%2B+3c+-+10.8c+%2B+7.8c+-+23.4+%2B+9+=+0+
(2) +3.6c%5E2+-+23.4+%2B+9+=+0+
(2) +3.6c%5E2+=+14.4+
(2) +c%5E2+=+4+
(2) +c+=+2+ mi/hr
The speed of the current is 2 mi/hr
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check the answer:
(1) +3+=+%28+3+-+c+%29%2At+
(1) +3+=+%28+3+-+2+%29%2At+
(1) +t+=+3+ hrs
and
(2) +3+=+%28+3+%2B+c+%29%2A%28+3.6+-+t+%29+
(2) +3+=+%28+3+%2B+2+%29%2A%28+3.6+-+t+%29+
(2) +3+=+5%2A%28+3.6+-+t+%29+
(2) +3+=+18+-+5t+
(2) +5t+=+15+
(2) +t+=+3+
and
notice that:
+t+%2B+%283.6+-+t%29+=+3+%2B+3.6+-+3+
and that = +3.6+ hrs which is the total time
Get another opinion if needed