document.write( "Question 1155509: A and b can paint a wall in 2 hours
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Algebra.Com's Answer #778114 by ikleyn(52778)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let a be the A's rate of work (the part of the job per hour).\r\n" );
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document.write( "Let b ve the B's rate of work;\r\n" );
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document.write( "and let c be the C's rate of work.\r\n" );
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document.write( "We have from the condition\r\n" );
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document.write( "    a + b = \"1%2F2\"    (1)\r\n" );
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document.write( "    a + c = \"1%2F3\"    (2)\r\n" );
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document.write( "    b + c = \"1%2F4\"    (3)\r\n" );
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document.write( "Add equations (1), (2) and (3) (both sides). You will fet\r\n" );
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document.write( "    2a + 2b + 2c = \"1%2F2+%2B+1%2F3+%2B+1%2F4\" = \"6%2F12+%2B+4%2F12+%2B+3%2F12\" = \"13%2F12\";\r\n" );
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document.write( "hence\r\n" );
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document.write( "    a + b + c = \"13%2F24\".    (4)\r\n" );
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document.write( "From equation (4), subtract equation (4).  You will get\r\n" );
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document.write( "    c = \"13%2F24+-+1%2F2\" = \"13%2F24+-+12%2F24\" = \"1%2F24\";  hence c = \"1%2F24\".\r\n" );
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document.write( "From equation (4), subtract equation (2).  You will get\r\n" );
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document.write( "    b = \"13%2F24+-+1%2F3\" = \"13%2F24+-+8%2F24\" = \"5%2F24\";  hence b = \"5%2F24\".\r\n" );
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document.write( "From equation (4), subtract equation (3).  You will get\r\n" );
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document.write( "    a = \"13%2F24+-+1%2F4\" = \"13%2F24+-+6%2F24\" = \"7%2F24\";  hence a = \"7%2F24\".\r\n" );
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document.write( "ANSWER.  It will take  \"24%2F7\" hours for A to complete the job working alone;\r\n" );
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document.write( "         It will take  \"24%2F5\" hours for B to complete the job working alone;\r\n" );
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document.write( "         It will take  \"24\" hours for C to complete the job working alone.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a classic and canonical way to solve this one and similar other problems for 3 participants.\r
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\n" ); document.write( "\n" ); document.write( "To see other solved problem by this method, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Selected joint-work word problems from the archive \r
\n" ); document.write( "\n" ); document.write( "    - Joint-work problems for 3 participants\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "It is a standard and typical ADVANCED joint work problem.\r
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\n" ); document.write( "\n" ); document.write( "There is a wide variety of solved joint-work problems with detailed explanations in this site.  See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Rate of work problems \r
\n" ); document.write( "\n" ); document.write( "    - Using Fractions to solve word problems on joint work \r
\n" ); document.write( "\n" ); document.write( "    - Solving more complicated word problems on joint work \r
\n" ); document.write( "\n" ); document.write( "    - Using quadratic equations to solve word problems on joint work \r
\n" ); document.write( "\n" ); document.write( "    - Solving rate of work problem by reducing to a system of linear equations \r
\n" ); document.write( "\n" ); document.write( "    - Solving joint work problems by reasoning \r
\n" ); document.write( "\n" ); document.write( "    - Selected joint-work word problems from the archive \r
\n" ); document.write( "\n" ); document.write( "    - Joint-work problems for 3 participants\r
\n" ); document.write( "\n" ); document.write( "    - Had there were more workers, the job would be completed sooner\r
\n" ); document.write( "\n" ); document.write( "    - One unusual joint work problem\r
\n" ); document.write( "\n" ); document.write( "    - Special joint work problems that admit and require an alternative solution method\r
\n" ); document.write( "\n" ); document.write( "    - Joint work word problems for the day of April, 1\r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on rate-of-work problems \r
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\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solving joint-work problems.\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 topic
\n" ); document.write( "\"Rate of work and joint work problems\"  of the section  \"Word problems\".\r
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\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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\n" ); document.write( "\n" ); document.write( "During several years, I developed and placed these lessons in this site.\r
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\n" ); document.write( "\n" ); document.write( "During several years I solved joint work problems and touched students and visitors to solve such problems\r
\n" ); document.write( "\n" ); document.write( "from introductory level to standard and typical level, and then from typical to advanced level, and then from advanced
\n" ); document.write( "to selected and challenging problems.\r
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\n" ); document.write( "\n" ); document.write( "Not only the visitors learned from my lessons --- the tutors themselves learned a lot from them.\r
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\n" ); document.write( "\n" ); document.write( "It was and it is a pleasure for me to see the growing interest to solving such problem, and to see the growing level of upcoming problems.\r
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\n" ); document.write( "\n" ); document.write( "Now I see that the most advanced of these lessons become a subject of interests for visitors.\r
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\n" ); document.write( "\n" ); document.write( "I am very glad and very proud to see this progress.\r
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