document.write( "Question 1111666: The crew of a rowing shell can row 8 miles downstream and back or 12 miles downstream and halfway back in 1 1/2 hours how fast can they row in still water? What is the velocity of the stream? \n" ); document.write( "

Algebra.Com's Answer #726672 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "Let u = the shell rate in still water (in miles per hour) and\r\n" );
document.write( "let v = the rate of the current.\r\n" );
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document.write( "Then you have TWO \"time\" equations\r\n" );
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document.write( " +  =     (1)    (\"8 miles downstream and back in 1 1/2 hours\")\r\n" );
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document.write( " +  =    (2)    (\"12 miles downstream and halfway back in 1 1/2 hours)\r\n" );
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document.write( "To solve the syste, introduce new variables  x = ,  y = .\r\n" );
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document.write( "Then the system takes the form\r\n" );
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document.write( " 8x + 8y = \r\n" );
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document.write( "12x + 6y = .\r\n" );
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document.write( "Simplify it to\r\n" );
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document.write( " x + y =     (3)\r\n" );
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document.write( "2x + y =     (4)\r\n" );
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document.write( "Subtract  eq(3)  from eq(4), eliminating \"y\".  You will get\r\n" );
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document.write( " x =  -  =  -  =  = .\r\n" );
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document.write( "Then from (3)  y =  -  =  = .\r\n" );
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document.write( "It implies\r\n" );
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document.write( "u + v =  = 16,   (5)\r\n" );
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document.write( "u - v =  =  8.   (6)\r\n" );
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document.write( "Add equations (5) and (6), eliminating \"v\". You will get\r\n" );
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document.write( "2u = 16 + 8 = 24  ====>  u =  = 12.\r\n" );
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document.write( "Then from eq(5)  v = 16 - 12 = 4.\r\n" );
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document.write( "Answer.  The speed of the shell in still water is  12 mph.  The current rate is 4 mph.\r\n" );
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\n" ); document.write( "It is a typical and standard Upstream and Downstream round trip word problem.\r
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\n" ); document.write( "\n" ); document.write( "You can find many similar fully solved problems on upstream and downstream round trips with detailed solutions and explanations 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
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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.\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
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\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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