Question 715595
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.


While A and B worked together for 5 days, amount of job done was {{{(1/12)*5}}}.


After the first 5 days, B worked separately alone,  and then C worked separately alone and finished:


Accounting for the 1 job done, {{{(1/12)*5+B*7+C*13=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+C=(1/16)}}}.  Those two equations give us a system using TWO variables.


SYSTEM TO SOLVE:
{{{highlight((1/12)*5+B*7+C*13=1)}}}
{{{highlight(B+C=(1/16))}}}
We can solve for B and C, or substitute to solve just for C, his rate of work.