document.write( "Question 1032377: Abe, Bart and Cain are house painters. It takes Abe and Bart 15 days to paint a house. It will take Bart and Cain 12 days to paint the same house while Abe and Cain will take 20 days for the same job. How many days will it take if 3 of them work together? \n" ); document.write( "

Algebra.Com's Answer #647072 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "Abe, Bart and Cain are house painters. It takes Abe and Bart 15 days to paint a house. It will take Bart and Cain 12 days to paint
\n" ); document.write( "the same house while Abe and Cain will take 20 days for the same job. How many days will it take if 3 of them work together?
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document.write( "Let \"a\", \"b\" and \"c\" be the rates of work of each of the boys Abe, Bart, and Cain respectively.\r\n" );
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document.write( "We are given that \r\n" );
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document.write( "a + b = ,    (1)\r\n" );
document.write( "a + c = ,    (2)\r\n" );
document.write( "b + c = .    (3)\r\n" );
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document.write( "To solve the problem, let us add the equations (1), (2) and (3).\r\n" );
document.write( "You will get \r\n" );
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document.write( "2a + 2b + 2c =  =  =  =  = .\r\n" );
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document.write( "Hence, \r\n" );
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document.write( "a + b + c = .\r\n" );
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document.write( "Thus we just found the combined rate-of-work of the three boys working togetther. It is  job per day.\r\n" );
document.write( "It implies that it will take 10 days for three boys to complete the job working together.\r\n" );
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document.write( "Answer.  10 days.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the solution of the similar problem presented in the lesson
\n" ); document.write( "Joint-work problems for 3 participants in this site.\r
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\n" ); document.write( "\n" ); document.write( "See also a variety of other solved joint-work problems in the lessons associated with it.\r
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