document.write( "Question 633499: John can do a piece of work in 15 days. John and David can do the same amount work in 6 days. In how many days David alone can do the same amount of work? \n" ); document.write( "

Algebra.Com's Answer #398945 by Edwin McCravy(20060) $\"\"$ $\"About$

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John can do a piece of work in 15 days. John and David can do the same amount work in 6 days. In how many days David alone can do the same amount of work?
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document.write( "There are two ways to do the problem: (1) in your head and (2) by algebra.\r\n" );
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document.write( "The first way is \"in your head\":\r\n" );
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document.write( "The LCM of 6 days and 15 days is 30 days.  So in 30 days John could do 2 pieces\r\n" );
document.write( "of work. And if they worked together for 30 days they could do 5 pieces of\r\n" );
document.write( "work.  So if they worked together for 30 days, John would do 2 pieces of work\r\n" );
document.write( "and therefore David would do the other 3 pieces of work.  Therefore David can\r\n" );
document.write( "do 3 pieces of work in 30 days, so he can do 1 piece of work in 10 days.\r\n" );
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document.write( "The second way is \"by algebra\":\r\n" );
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document.write( "Make this chart:\r\n" );
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document.write( "            jobs done          time in days       rate in jobs/day\r\n" );
document.write( "John\r\n" );
document.write( "David\r\n" );
document.write( "together\r\n" );
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document.write( "John can do 1 job in 15 days, so we fill in 1 for his jobs done and 15\r\n" );
document.write( "for his time in days:\r\n" );
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document.write( "            jobs done          time in days       rate in jobs/day\r\n" );
document.write( "John            1                   15                    \r\n" );
document.write( "David\r\n" );
document.write( "together\r\n" );
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document.write( "John and David together can do 1 job in 6 days, so we fill in 1 for his jobs\r\n" );
document.write( "done and 6 for their time in days:\r\n" );
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document.write( "            jobs done          time in days       rate in jobs/day\r\n" );
document.write( "John            1                   15                    \r\n" );
document.write( "David\r\n" );
document.write( "together        1                    6                  \r\n" );
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document.write( "Let x = the number of days it would take David alone to do one piece of\r\n" );
document.write( "work. So we fill in 1 for David's jobs done and x for his time in days:\r\n" );
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document.write( "            jobs done          time in days       rate in jobs/day\r\n" );
document.write( "John            1                   15                    \r\n" );
document.write( "David           1                    x\r\n" );
document.write( "together        1                    6 \r\n" );
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document.write( "Next we fill in the three rates in jobs/day by putting jobs over days:\r\n" );
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document.write( "            jobs done          time in days       rate in jobs/day\r\n" );
document.write( "John            1                   15                 1/15                    \r\n" );
document.write( "David           1                    x                  1/x\r\n" );
document.write( "together        1                    6                  1/6\r\n" );
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document.write( "             \r\n" );
document.write( "        The equation comes from the sum of their rates equals their\r\n" );
document.write( "combined rate:\r\n" );
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document.write( "                  +  = \r\n" );
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document.write( "                  +  = \r\n" );
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document.write( "Get an LCD of 30x and multiply through and the answer will be x=10 days,\r\n" );
document.write( "the same answer as when we do it in our head.\r\n" );
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document.write( "Edwin

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