SOLUTION: 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

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?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= fraction of the job A can do in 1 day.
= fraction of the job B can do in 1 day.
= fraction of the job C can do in 1 day.

"A and B together can do a piece of work in 12 days" translates as
<---><---> .
Since that is a job "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" translates as
.
You get the system
<---> .
If you add all 3 equations, you get
--->--->---> .
Since C can do of the joy each day,
C alone will do the work in .

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