document.write( "Question 1145794: A, B and C can do a piece of work in 10 days. A and B can do it in 12 days, and A and C in 20 days. How many days would it take each to do the work place? \n" ); document.write( "

Algebra.Com's Answer #767046 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let \"a\" be the rate of work of \"A\";\r\n" );
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document.write( "    \"b\" be the rate of work of \"B\";  and\r\n" );
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document.write( "    \"c\" be the rate of work of \"C\".\r\n" );
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document.write( "Then, according to the condition, you have this system of 3 equations in 3 unknowns\r\n" );
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document.write( "    a + b =        (1)\r\n" );
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document.write( "    a + c =        (2)\r\n" );
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document.write( "    a + b + c =    (3)\r\n" );
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document.write( "To solve the system of equations, first subtract equation (1) from equation (3). You will get\r\n" );
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document.write( "    c =  -  =  = .\r\n" );
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document.write( "It means that \"C\" will do the work in 60 days, working alone.\r\n" );
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document.write( "Next, subtract equation (2) from equation (3). You will get\r\n" );
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document.write( "    b =  -  =  = .\r\n" );
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document.write( "It means that \"B\" will do the work in 20 days, working alone.\r\n" );
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document.write( "Finally, substitute  b=  into equation (1) and get \"a\"\r\n" );
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document.write( "    a =  -  =  =  = .\r\n" );
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document.write( "ANSWER.  A can do the work in 30 days, working alone.\r\n" );
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document.write( "         B can do the work in 20 days, working alone.\r\n" );
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document.write( "         C can do the work in 60 days, working alone.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a standard and typical joint work problem for 3 participants.\r
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\n" ); document.write( "\n" ); document.write( "In this site, there is a bunch of lessons on joint worl problems, from simple to more complicated and advanced.\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 get be trained in solving joint-work problems.\r
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\n" ); document.write( "\n" ); document.write( "The most closed to your problem is the lesson marked (*) in the list.
\n" ); document.write( "You will find there other similar solved 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( "Come to this forum again soon to learn something new (!)\r
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