nice answer devilmirror, but i'm not sure if it accurately represents the stem:
"After A has been working at it for 5 Days and B for 7 Days", then C has 13 days left...
It seems to me that A,B and C work as in a sequence: first A, second B and then C.
ARe you sure that A and B can work together?
Altough, A, B, and C work as sequence but you can consider them working to gether on the same days and use the rate provide from the question. Just keep in mind that the time that they work will be 2 time faster.
Here the prove.
Assuming A's work rate = 1/a (work/day)
Assuming B's work rate = 1/b (work/day)
If A works for T day the work that A does = T/a work
If B also works for T day the work that B does = T/b work
Total work done = T/a + T/b
However, if A and B working together they will use T day to finish this job.
Work rate = (T/a + T/b)/T = (1/a + 1/b)
The equation above is the work rate of A + B combined!
Therefore, we can safely conclude that.
If A work on T day and B work on T day seperately, this will equal to A and B working together for T day.
Using the prove above to solve that question and the answer is 24.