document.write( "Question 1204175: P can complete a task in x days while Q takes (x + 12) days to do the same task.
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\n" ); document.write( "complete the task in 8 days. Find x. \n" ); document.write( "

Algebra.Com's Answer #840250 by Edwin McCravy(20056) $\"\"$ $\"About$

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P can complete a task in x days while Q takes (x + 12) days to do the same task.
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document.write( "P can complete 1 task in x days, so P can complete 1/x of a task in 1 day.\r\n" );
document.write( "Q can complete 1 task in (x + 12) days, so Q can complete 1/(x + 12) of a task\r\n" );
document.write( "in 1 day.

\n" ); document.write( "b) If both of them work together, they can
\n" ); document.write( "complete the task in 8 days. Find x.

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document.write( "P can complete 1/x of a task in 1 day, so P can complete 8/x of a task in 8\r\n" );
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document.write( "Q can complete 1/(x + 12) of a task in 1 day, so Q can complete 8/(x + 12) of a\r\n" );
document.write( "task in 8 days.\r\n" );
document.write( "So together, they can complete 8/x + 8/(x+12) of a task in 8 days\r\n" );
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document.write( "That's 1 task, so \r\n" );
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document.write( "LCD = x(x + 12)\r\n" );
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document.write( "x+8=0; x-12=0\r\n" );
document.write( "  x=-8;   x=12\r\n" );
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document.write( "x cannot be negative.\r\n" );
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document.write( "x = 12.\r\n" );
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document.write( "Now that we have x, we can answer (a) as a numerical fraction:\r\n" );
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document.write( "a) What fraction of the task can each of them complete in a day?\r\n" );
document.write( "P can complete 1 task in 12 days, so P can complete 1/12 of a task in 1 day.\r\n" );
document.write( "Q can complete 1 task in (12 + 12) = 24 days, so Q can complete 1/(12 + 12) = 1/24 of a task in 1 day.
Edwin

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