document.write( "Question 1058038: Jack and Jill together can do a piece of work in 3 days.
\n" ); document.write( "They can finish the work if Jack works for 2 days and Jill
\n" ); document.write( "works for 4 days. Find the time required for each to do the
\n" ); document.write( "work. \n" ); document.write( "
Algebra.Com's Answer #673071 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Jack and Jill together can do a piece of work in 3 days.
\n" ); document.write( "They can finish the work if Jack works for 2 days and Jill
\n" ); document.write( "works for 4 days. Find the time required for each to do the
\n" ); document.write( "work.
\n" ); document.write( "
\r\n" );
document.write( "Let the time for Jack to do the job = x days\r\n" );
document.write( "\r\n" );
document.write( "So Jack's rate in jobs per day is\r\n" );
document.write( "\r\n" );
document.write( "1 job per x days or\r\n" );
document.write( "\r\n" );
document.write( "\"matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2Cx%2Cdays%29\",\r\n" );
document.write( "\r\n" );
document.write( "so his rate in jobs/day is \r\n" );
document.write( "\r\n" );
document.write( "\"matrix%281%2C2%2C1%2Fx%2Cjobs%2Fday%29\"\r\n" );
document.write( "\r\n" );
document.write( "---\r\n" );
document.write( "\r\n" );
document.write( "Let the time for Jill to do the job = y days\r\n" );
document.write( "\r\n" );
document.write( "So Jill's rate in jobs per day is\r\n" );
document.write( "\r\n" );
document.write( "1 job per y days or\r\n" );
document.write( "\r\n" );
document.write( "\"matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2Cy%2Cdays%29\",\r\n" );
document.write( "\r\n" );
document.write( "so her rate in jobs/day is \r\n" );
document.write( "\r\n" );
document.write( "\"matrix%281%2C2%2C1%2Fy%2Cjobs%2Fday%29\"\r\n" );
document.write( "\r\n" );
document.write( "We look at the second sentence first:\r\n" );
document.write( "

\n" ); document.write( "They can finish the work if Jack works for 2 days
\n" ); document.write( "and Jill works for 4 days.
\n" ); document.write( "
\r\n" );
document.write( "In 2 days, using \r\n" );
document.write( "\r\n" );
document.write( "production = rate × time, Jack's production = \"2%2A%281%2Fx%29\" or \"2%2Fx\".\r\n" );
document.write( "\r\n" );
document.write( "In 4 days, using \r\n" );
document.write( "\r\n" );
document.write( "production = rate × time, Jill's production = \"4%2A%281%2Fy%29\" or \"4%2Fy\".\r\n" );
document.write( "\r\n" );
document.write( "Since they finish 1 job, \r\n" );
document.write( "\r\n" );
document.write( "\"2%2Fx%2B4%2Fy\"\"%22%22=%22%22\"\"1\"\r\n" );
document.write( "\r\n" );
document.write( "Now we look at the first sentence:\r\n" );
document.write( "

\n" ); document.write( "Jack and Jill together can do a piece of work in 3 days.
\n" ); document.write( "
\r\n" );
document.write( "Their combined rate is the sum of their rates, so\r\n" );
document.write( "\r\n" );
document.write( "Their combined rate = \"1%2Fx%2B1%2Fy\"\r\n" );
document.write( "\r\n" );
document.write( "So in 3 days, using \r\n" );
document.write( "\r\n" );
document.write( "production = rate × time, the production = \"3%2A%281%2Fx%2B1%2Fy%29\" or \"3%2Fx%2B3%2Fy\".\r\n" );
document.write( "\r\n" );
document.write( "Since they finish 1 job, \r\n" );
document.write( "\r\n" );
document.write( "\"3%2Fx%2B3%2Fy\"\"%22%22=%22%22\"\"1\"\r\n" );
document.write( "\r\n" );
document.write( "So the system of equations is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Adding them term by term gives:\r\n" );
document.write( "\r\n" );
document.write( "\"6%2Fy=1\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by y\r\n" );
document.write( "\r\n" );
document.write( "\"6=y\"\r\n" );
document.write( "\r\n" );
document.write( "So Jack can do the job in 6 days.\r\n" );
document.write( "\r\n" );
document.write( "Substituting y=6 in\r\n" );
document.write( "\r\n" );
document.write( "\"2%2Fx%2B4%2Fy=1\"\r\n" );
document.write( "\r\n" );
document.write( "\"2%2Fx%2B4%2F6=1\"\r\n" );
document.write( "\r\n" );
document.write( "\"2%2Fx%2B2%2F3=1\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by 3x\r\n" );
document.write( "\r\n" );
document.write( "\"6%2B2y=3x\"\r\n" );
document.write( "\r\n" );
document.write( "\"6=y\"\r\n" );
document.write( "\r\n" );
document.write( "So Jill can also do the job in 6 days.\r\n" );
document.write( "\r\n" );
document.write( "They can each do the job working alone in 6 days.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );