SOLUTION: A boy can row a boat a constant rate of 5 mi/hr in still water. He rows upstream 28 minutes and then travels downstream returning to his starting point in another 12 minutes. upstr

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Question 993248: A boy can row a boat a constant rate of 5 mi/hr in still water. He rows upstream 28 minutes and then travels downstream returning to his starting point in another 12 minutes. upstream net speed equals 5 - x miles per hourand downstream net speed equals 5 plus x miles per hourfind the right of the current in miles per hour find the total distance traveled in miles
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+28+ min
+28%2F60+=+7%2F15+ hr
and
+12+ min
+12%2F60+=+1%2F5+ hr
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Equation for rowing upstream:
(1) +d+=+%28+5+-+x+%29%2A%28+7%2F15+%29+
Equation for rowing downstream:
(2) +d+=+%28+5+%2B+x+%29%2A%28+1%2F5+%29+
---------------------------
(1) +d+=+7%2F3+-+%28+7%2F15+%29%2Ax+
and
(2) +d+=+1+%2B+%28+1%2F5+%29%2Ax+
------------------------
Substitute (1) into (2)
(2) +7%2F3+-+%28+7%2F15+%29%2Ax+=+1+%2B+%28+1%2F5+%29%2Ax+
Multiply both sides by +15+
(2) +35+-+7x+=+15+%2B+3x+
(2) +10x+=+20+
(2) +x+=+2+
----------------
The speed of the current is 2 mi/hr
----------------
(2) +d+=+1+%2B+%28+1%2F5+%29%2Ax+
(2) +d+=+1+%2B+%28+1%2F5+%29%2A2+
(2) +d+=+1.4+
--------------
The 2-way distance is +2%2A1.4+=+2.8+
2.8 mi total distance traveled
-------------------------
check:
(1) +d+=+%28+5+-+x+%29%2A%28+7%2F15+%29+
(1) +1.4+=+%28+5+-+2+%29%2A%28+7%2F15+%29+
(1) +1.4+=+7%2F5+
(1) +1.4+=+1.4+
OK