document.write( "Question 1188240: Hi! I've been trying this problem for some time and I can't seem to figure it out.\r
\n" ); document.write( "\n" ); document.write( "A mechanical sorter can process a bag of mail in 18 minutes. After the sorter has been working for some time, it breaks down. The rest of the mail it was sorting is divided equally between two older machines, each of which would take 60 minutes to complete the job working alone. The mail is finished being sorted 20 minutes after the first machine started working. How long did the first machine work before breaking down?\r
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Algebra.Com's Answer #819307 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!
Hi! I've been trying this problem for some time and I can't seem to figure it out.\r
\n" ); document.write( "\n" ); document.write( "A mechanical sorter can process a bag of mail in 18 minutes. After the sorter has been working for some time, it breaks down. The rest of the mail it was sorting is divided equally between two older machines, each of which would take 60 minutes to complete the job working alone. The mail is finished being sorted 20 minutes after the first machine started working. How long did the first machine work before breaking down?\r
\n" ); document.write( "\n" ); document.write( "Thank you! :)
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Let the time that the first machine worked, be T\r\n" );
document.write( "Since the total time taken to do the entire job was 20 minutes, the time the 2 other machines took was \"20 - T\" minutes\r\n" );
document.write( "At 18 minutes to complete the job, first machine's rate is \"1%2F18\"\r\n" );
document.write( "Fraction of work completed by first machine before breaking down: \"matrix%281%2C3%2C+T%281%2F18%29%2C+or%2C+T%2F18%29\"\r\n" );
document.write( "At 60 minutes to complete the job, each of the other 2 machines' rate is \"1%2F60\", and both have a rate of \"matrix%281%2C5%2C+1%2F60+%2B+1%2F60%2C+%22=%22%2C+2%2F60%2C+%22=%22%2C+1%2F30%29\"\r\n" );
document.write( "Fraction of work completed by other 2 machines after first broke down: \"matrix%281%2C3%2C+%2820+-+T%29%281%2F30%29%2C+or%2C+%2820+-+T%29%2F30%29\"\r\n" );
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document.write( "With the entire job being completed by the 3 machines in 20 minutes, we get: \"matrix%281%2C3%2C+T%2F18+%2B+%2820+-+T%29%2F30%2C+%22=%22%2C+1%29\"\r\n" );
document.write( "5T + 3(20 - T) = 90 ------ Multiplying by LCD, 90\r\n" );
document.write( "5T + 60 - 3T = 90\r\n" );
document.write( "5T - 3T = 90 - 60\r\n" );
document.write( "2T = 30\r\n" );
document.write( "Time that the first machine worked, or \"highlight_green%28matrix%281%2C6%2C+T%2C+%22=%22%2C+30%2F2%2C+%22=%22%2C+15%2C+minutes%29%29\"\r\n" );
document.write( "You can do the check!!
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