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 #647035 by Edwin McCravy(20056) $\"\"$ $\"About$

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Abe, Bart and Cain are house painters. It takes Abe
\n" ); document.write( "and Bart 15 days to paint a house. It will take Bart
\n" ); document.write( "and Cain 12 days to paint the same house while Abe
\n" ); document.write( "and Cain will take 20 days for the same job. How many
\n" ); document.write( "days will it take if 3 of them work together?
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document.write( "Suppose Abe can paint a house by himself in A days.\r\n" );
document.write( "Then Abe's painting rate is \r\n" );
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document.write( "1 house in A days =    \r\n" );
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document.write( "Suppose Bart can paint a house by himself in B days.\r\n" );
document.write( "Then Bart's painting rate is \r\n" );
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document.write( "1 house in B days =  \r\n" );
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document.write( "Suppose Cain can paint a house by himself in C days.\r\n" );
document.write( "Then his painting rate is \r\n" );
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document.write( "1 house in C days =  \r\n" );
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\n" ); document.write( "It takes Abe and Bart 15 days to paint a house.....
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\r\n" );
document.write( "So the sum of Abe's and Bart's rates equals 1 house per 15 days.\r\n" );
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document.write( "That's 1 house in 15 days =  \r\n" );
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document.write( "So \r\n" );
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\n" ); document.write( "It will take Bart and Cain 12 days to paint the same house....
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\r\n" );
document.write( "So the sum of Bart's and Cain's rates equals 1 house per 12 days.\r\n" );
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document.write( "That's 1 house in 12 days =  \r\n" );
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document.write( "So \r\n" );
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\n" ); document.write( "while Abe and Cain will take 20 days for the same job.
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\r\n" );
document.write( "So the sum of Abe's's and Cain's rates equals 1 house per 20 days.\r\n" );
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document.write( "That's 1 house in 20 days =  \r\n" );
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document.write( "So \r\n" );
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document.write( "So we have this system of three equations:\r\n" );
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document.write( "Subtracting the first two equations:\r\n" );
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document.write( "Adding that to the third equation:\r\n" );
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document.write( "-------------\r\n" );
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document.write( "Multiplying both sides of\r\n" );
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document.write( " by 1/2 gives:\r\n" );
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document.write( "-------------------\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "  \r\n" );
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document.write( "Substituting\r\n" );
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document.write( "in\r\n" );
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document.write( "

\n" ); document.write( "How many days will it take if 3 of them work together
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\r\n" );
document.write( "Suppose working together they can paint a house in D days.\r\n" );
document.write( "Then their combined painting rate is \r\n" );
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document.write( "1 house in D days = \r\n" );
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document.write( "Then the sum of their painting rates will equal 1/D:\r\n" );
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document.write( "It will take them 10 days.\r\n" );
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document.write( "Edwin

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