document.write( "Question 582314: Mary and Jane could finish a job in 1 hour. After Mary worked in the job for 2 hours, Jane joined her and together they finished the job in 20 minutes. How long will each of them finish the job working alone?\r
\n" ); document.write( "\n" ); document.write( "*please answer the problem with 2 equations and 2 unknowns(x and y). thanks! \n" ); document.write( "
Algebra.Com's Answer #372036 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Mary and Jane could finish a job in 1 hour. After Mary worked in the job for 2 hours, Jane joined her and together they finished the job in 20 minutes. How long will each of them finish the job working alone?\r
\n" ); document.write( "\n" ); document.write( "*please answer the problem with 2 equations and 2 unknowns(x and y). thanks!
\n" ); document.write( "
\r\n" );
document.write( "Let x = the number of hours it would take Mary to finish 1 job working alone.\r\n" );
document.write( "Let y = the number of hours it would take Jane to finish 1 job working alone.\r\n" );
document.write( "\r\n" );
document.write( "20 minutes = 1/3 hour\r\n" );
document.write( "\r\n" );
document.write( "Make this chart:\r\n" );
document.write( "                          No. of jobs     No. of      Rate \r\n" );
document.write( "                          or fraction     hours        in\r\n" );
document.write( "                          thereof         worker    jobs/hour\r\n" );
document.write( "M. alone for x hours           1            x\r\n" );
document.write( "J. alone for y hours           1            y\r\n" );
document.write( "M. and J. together for 1 hr    1            1          1\r\n" );
document.write( "M. alone for 2 hours                        2\r\n" );
document.write( "M. and J. together for 1/3 hr              1/3\r\n" );
document.write( "\r\n" );
document.write( "Fill in the rates in jobs/hour in the first two cases by dividing\r\n" );
document.write( "jobs done by the number of hours:\r\n" );
document.write( "\r\n" );
document.write( "                          No. of jobs     No. of      Rate \r\n" );
document.write( "                          or fraction     hours        in\r\n" );
document.write( "                          thereof         worker    jobs/hour\r\n" );
document.write( "M. alone for x hours           1            x         1/x\r\n" );
document.write( "J. alone for y hours           1            y         1/y\r\n" );
document.write( "M. and J. together for 1 hr    1            1          1\r\n" );
document.write( "M. alone for 2 hours                        2\r\n" );
document.write( "M. and J. together for 1/3 hr              1/3\r\n" );
document.write( "\r\n" );
document.write( "We can now fill in M's rate working alone for 2 hours as the same\r\n" );
document.write( "rate 1/x.  We can also fill in the rate of them working together for\r\n" );
document.write( "1/3 hour as the same 1 job/hour rate as when they work for 1 hour.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                          No. of jobs     No. of      Rate \r\n" );
document.write( "                          or fraction     hours        in\r\n" );
document.write( "                          thereof         worker    jobs/hour\r\n" );
document.write( "M. alone for x hours           1            x         1/x\r\n" );
document.write( "J. alone for y hours           1            y         1/y\r\n" );
document.write( "M. and J. together for 1 hr    1            1          1\r\n" );
document.write( "M. alone for 2 hours                        2         1/x\r\n" );
document.write( "M. and J. together for 1/3 hr              1/3         1\r\n" );
document.write( "  \r\n" );
document.write( "Now we can fill in the no. of jobs or fraction thereof (actually fraction\r\n" );
document.write( "tereof) that M. did alone for 2 hours by multiplying her rate times her\r\n" );
document.write( "time (2 hours) getting 2/x.  Similar we can fill in the fraction of a \r\n" );
document.write( "job that they did together in 1/3 hour by multiplying their combined \r\n" );
document.write( "rate 1 job/hour by 1/3 hour.\r\n" );
document.write( "\r\n" );
document.write( "                             No. of jobs     No. of      Rate \r\n" );
document.write( "                             or fraction     hours        in\r\n" );
document.write( "                             thereof         worker    jobs/hour\r\n" );
document.write( "M. alone for x hours              1            x         1/x\r\n" );
document.write( "J. alone for y hours              1            y         1/y\r\n" );
document.write( "M. and J. together for 1 hr       1            1          1\r\n" );
document.write( "M. alone for 2 hours             2/x           2         1/x\r\n" );
document.write( "M. and J. together for 1/3 hr    1/3          1/3         1\r\n" );
document.write( "\r\n" );
document.write( "Our two equations come from:\r\n" );
document.write( "\r\n" );
document.write( "             \"%28matrix%284%2C1%2C%0D%0A%0D%0A%22Mary%27s%22%2Crate%2Cworking%2Calone%29%29\" + \"%28matrix%284%2C1%2C%0D%0A%0D%0A%22Jane%27s%22%2Crate%2Cworking%2Calone%29%29\" = \"%28matrix%285%2C1%2C%0D%0A%0D%0ATheir%2Ccombined%2Crate%2Cworking%2Ctogether%29%29\" \r\n" );
document.write( "\r\n" );
document.write( "              +  = \"%28matrix%283%2C1%2C%0D%0A%0D%0A1%2Ccomplete%2C+job%29%29\" \r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "            \"1%2Fx\" + \"1%2Fy\" = \"1\" \r\n" );
document.write( "            \"2%2Fx\" + \"1%2F3\" = \"1\"\r\n" );
document.write( "\r\n" );
document.write( "Solve that system and get x = 3 and y = \"3%2F2\" or 1.5 hours\r\n" );
document.write( "\r\n" );
document.write( "So Mary takes 3 hourse to do the job and Jane takes 1.5 hours\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );