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A and B together can do a peace of work in 12 days,which B [#permalink]
05 Feb 2007, 10:30

A and B together can do a peace 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?

A and B together can do a peace 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?

Assuming everybody works at constant rate and independent from each other.

When A works for 5 days and B works for 7 days, we can conclude that A and B work together for 5 days and B works alone for 2 days. And

Work Rate(A+B) = 1/12 (work/day)

Thus, Work is done by A and B for 5 days together = 5 days x 1/12 (work/day) = 5/12 work

When B works for 7-5 = 2 days and C works for 13 day, we can conclude that B and C work together for 2 days and C work alone for 13 - 2 = 11 days.

Work Rate(B+C) = 1/16 (work/day)

Thus, Work is done by B and C for 2 days = 2 days x 1/16 (work/day) = 1/8 work

The remaining job = 1 - 5/12 - 1/8 = (24 - 10 - 3)/24 = 11/24 work

C can finish this part of work within 11 days. Therefore, the work rate for C = 11/24 (work) x 1/11(1/day) = 1/24 (work/day)

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?

Hi pau.sabria,

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.