document.write( "Question 1199268: Jay can do a painting job in 2/3 as many days as Chris can, and Chris can do it in 3/4 as many days as Araceli can. If all three work together, they can do it in 36/13 days. In how many days can each of them alone do the work? \n" ); document.write( "

Algebra.Com's Answer #833069 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( "Jay can do a painting job in 2/3 as many days as Chris can,
\n" ); document.write( "and Chris can do it in 3/4 as many days as Araceli can.
\n" ); document.write( "If all three work together, they can do it in 36/13 days.
\n" ); document.write( "In how many days can each of them alone do the work?
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document.write( "Let \"a\" be the Araceli's rate of work.\r\n" );
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document.write( "Then Chris' rate of work is  , and Jay's rate of work is .\r\n" );
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document.write( "Their combined rate of work is then \r\n" );
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document.write( "    a +  +  = a +  + 2a =  = .\r\n" );
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document.write( "From the other side, their combined rate of work is  .\r\n" );
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document.write( "It gives us this equation\r\n" );
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document.write( "     = .\r\n" );
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document.write( "From this equation,  a = .\r\n" );
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document.write( "Thus Araceli can make the job in 12 days, working alone; Cris can make it in   = 9 days\r\n" );
document.write( "and Jay can make it in   = 6 days.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a standard and typical joint work problem.\r
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\n" ); document.write( "\n" ); document.write( "There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons\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( "    - Selected joint-work word problems from the archive \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( "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
\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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