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 #819277 by ikleyn(52786)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "A mechanical sorter can process a bag of mail in 18 minutes.
\n" ); document.write( "After the sorter has been working for some time, it breaks down.
\n" ); document.write( "The rest of the mail it was sorting is divided equally between two older machines,
\n" ); document.write( "each of which would take 60 minutes to complete the job working alone.
\n" ); document.write( "The mail is finished being sorted 20 minutes after the first machine started working.
\n" ); document.write( "How long did the first machine work before breaking down?
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document.write( "Let \"t\" be the time under the problem's question, in minutes.\r\n" );
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document.write( "First sorter did  \"t%2F18\"  part of the job before breaking.\r\n" );
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document.write( "Two other machines worked 20-t minutes each, and these two machines did  \"2%2A%28%2820-t%29%2F60%29\"  parts of the job.\r\n" );
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document.write( "The multiplier 2 reflects the fact that TWO machines worked during these 20-t minutes.\r\n" );
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document.write( "The \"total job\" equation is\r\n" );
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document.write( "    \"t%2F18\" + \"2%2A%28%2820-t%29%2F60%29\" = 1.\r\n" );
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document.write( "Multiply both sides by 180; then simplify and find \"t\"\r\n" );
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document.write( "    10t + 6*(20-t) = 180\r\n" );
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document.write( "    10t + 120 - 6t = 180\r\n" );
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document.write( "       4t          = 180 - 120 = 60\r\n" );
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document.write( "        t          = \"60%2F4\" = 15 minutes.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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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
\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
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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
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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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