SOLUTION: 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 tot

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 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 tot      Log On


   

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 .
Answer by josgarithmetic(39616) About Me  (Show Source):
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.

While A and B worked together for 5 days, amount of job done was %281%2F12%29%2A5.

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

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.

SYSTEM TO SOLVE:
highlight%28%281%2F12%29%2A5%2BB%2A7%2BC%2A13=1%29
highlight%28B%2BC=%281%2F16%29%29
We can solve for B and C, or substitute to solve just for C, his rate of work.