document.write( "Question 934977: A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes in 13 days. In how many days C alone will do the work? \n" ); document.write( "

Algebra.Com's Answer #568022 by KMST(5328) $\"\"$ $\"About$

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$\"a\"$ = fraction of the job A can do in 1 day.
\n" ); document.write( " $\"b\"$ = fraction of the job B can do in 1 day.
\n" ); document.write( " $\"c\"$ = fraction of the job C can do in 1 day.
\n" ); document.write( "
\n" ); document.write( "\"A and B together can do a piece of work in 12 days\" translates as
\n" ); document.write( " $\"12%28a%2Bb%29=1\"$ <---> $\"12a%2B12b=1\"$ <---> $\"a%2Bb=1%2F12\"$ .
\n" ); document.write( "Since that is a job \"which B and C together can do in 16 days\" ,
\n" ); document.write( " $\"16%28b%2Bc%29=1\"$ <---> $\"16b%2B16c=1\"$ <---> $\"b%2Bc=1%2F16\"$ .
\n" ); document.write( "\"After A has been working at it for 5 days and B for 7 days, C finishes in 13 days\" translates as
\n" ); document.write( " $\"5a%2B7b%2B13c=1\"$ .
\n" ); document.write( "You get the system
\n" ); document.write( " $\"system%28a%2Bb=1%2F12%2Cb%2Bc=1%2F16%2C5a%2B7b%2B13c=1%29\"$ <---> $\"system%28-5a-5b=-5%2F12%2C-2b-2c=-1%2F8%2C5a%2B7b%2B13c=1%29\"$ .
\n" ); document.write( "If you add all 3 equations, you get
\n" ); document.write( " $\"13c-2c=1-5%2F12-1%2F8\"$ ---> $\"11c=24%2F24-10%2F24-3%2F24\"$ ---> $\"11c=11%2F24\"$ ---> $\"c=1%2F24\"$ .
\n" ); document.write( "Since C can do $\"1%2F24\"$ of the joy each day,
\n" ); document.write( "C alone will do the work in $\"highlight%2824+days%29\"$ .
\n" ); document.write( " \n" ); document.write( "

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