document.write( "Question 715595: A and B can do a job in 12 days and B and C can do it in 16 days. A and B started working, without C. A worked for 5 days and quit. B worked for 7 days and quit. C worked for a total of 13 days and finished the work. In how many days c alone can do the work . \n" ); document.write( "

Algebra.Com's Answer #439514 by josgarithmetic(39616) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the rates of work for each worker be A, B, and C, according to the name of each worker. Rate*Days=Jobs, and Rate is in jobs per day.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "While A and B worked together for 5 days, amount of job done was $\"%281%2F12%29%2A5\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "After the first 5 days, B worked separately alone, and then C worked separately alone and finished:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Accounting for the 1 job done, $\"%281%2F12%29%2A5%2BB%2A7%2BC%2A13=1\"$ . We ALSO have the given information of the combined rates of B and C. When they work together they do the job in 16 days, so we have $\"B%2BC=%281%2F16%29\"$ . Those two equations give us a system using TWO variables.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "SYSTEM TO SOLVE:
\n" ); document.write( " $\"highlight%28%281%2F12%29%2A5%2BB%2A7%2BC%2A13=1%29\"$
\n" ); document.write( " $\"highlight%28B%2BC=%281%2F16%29%29\"$
\n" ); document.write( "We can solve for B and C, or substitute to solve just for C, his rate of work. \n" ); document.write( "

\n" );