document.write( "Question 1111883: A student rows at a constant speed (relative to the water) downstream in the Nambucca River from Bowraville to Macksville, which takes 3 hours, and back upstream in 4 hours. If the river flows at a constant rate, find the number of hours it would take a piece of driftwood to float downstream from Bowraville to Macksville. \n" ); document.write( "

Algebra.Com's Answer #726917 by ikleyn(52816) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let L be the distance between the cities (in some units, miles or kilometers - IT DOES NOT MATTER, as you will see further).\r\n" );
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document.write( "Let u be the speed of the boat in still water (in the CORRESPONDING units), and\r\n" );
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document.write( "let v be the rate of the current (in the same units).\r\n" );
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document.write( "You are given\r\n" );
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document.write( " = 3  hours    (1)   (rowing downstream)\r\n" );
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document.write( " = 4  hours    (2)   (rowing   upstream)\r\n" );
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document.write( "From these equations\r\n" );
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document.write( "3*(u+v) = L                 (1')\r\n" );
document.write( "4*(u-v) = L                 (2')\r\n" );
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document.write( "or, equivalently\r\n" );
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document.write( "3u + 3v = L                 {1'')\r\n" );
document.write( "4u - 4v = L                 (2'')\r\n" );
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document.write( "What I need is to find the ratio  .  It is EXACTLY the time a piece of driftwood to float downstream from Bowraville to Macksville,\r\n" );
document.write( "which is under the question.\r\n" );
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document.write( "For it, I am going to eliminate the variable \"u\" from the equations (1'') and (2'') and to express \"v\" via L (or, conversely, express L via \"v\").\r\n" );
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document.write( "So I multiply eq(1'') by 4 (both sides) and multiply eq(2'') by 3 (both sides). I will get\r\n" );
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document.write( "12u - 12v = 3L     (3)\r\n" );
document.write( "12u + 12v = 4L     (4)\r\n" );
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document.write( "Now subtract eq(3) from eq(4). You will get\r\n" );
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document.write( "24v = L,   which implies   = 24.\r\n" );
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document.write( "It gives the ANSWER:  it will take 24 hours for a piece of driftwood to float downstream from Bowraville to Macksville\r\n" );
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document.write( "(since this piece moves with the rate of the current).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "-----------------
\n" ); document.write( "It is a CLASSIC \"downstream-upstream\" problem.\r
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Unpowered raft floating downstream along a river\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "You can find many other fully solved problems on upstream and downstream round trips with detailed solutions in lessons \r
\n" ); document.write( "\n" ); document.write( "    - Wind and Current problems \r
\n" ); document.write( "\n" ); document.write( "    - More problems on upstream and downstream round trips \r
\n" ); document.write( "\n" ); document.write( "    - Wind and Current problems solvable by quadratic equations \r
\n" ); document.write( "\n" ); document.write( "    - Unpowered raft floating downstream along a river (*)\r
\n" ); document.write( "\n" ); document.write( "    - Selected problems from the archive on the boat floating Upstream and Downstream \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Read them attentively and learn how to solve this type of problems once and for all.
\n" ); document.write( "The relevant lesson is marked (*) in this list.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the section \"Word problems\", the topic \"Travel and Distance problems\".\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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