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

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) (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 .

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

Accounting for the 1 job done, . 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 . Those two equations give us a system using TWO variables.

SYSTEM TO SOLVE:

We can solve for B and C, or substitute to solve just for C, his rate of work.
RELATED QUESTIONS
A,B and C can finish a job in 6 days. If B and C work together, the job will take 9 days; (answered by stanbon,harshachittar)

A and B together can do a piece of work in 12 days, which B and C together can do in 16... (answered by KMST)

Working alone, two painters, A and B, can paint a building in 12 and 16 days... (answered by ankor@dixie-net.com)

. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how... (answered by ankor@dixie-net.com)

If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how... (answered by jorel1380)

A can complete a job in 9 days, B can do the same job in 10 days and C can do it in 15... (answered by richwmiller)

a and b working together can do a given job in 4 days, b and c together can do the job in (answered by josgarithmetic,ikleyn)

A can do a piece of work in 16 days and B can do it in 20 days. These worked together for (answered by robertb)

A and B together can do a job in 12 days, and B and C together can do the same job in 16... (answered by richwmiller)