I'm stuck on a particular type of work and time problems.
1) A,B,C can complete a work separately in 24,36 and 48 days. They started working together but C left after 4 days of start and A left 3 days before completion of the work. In how many days will the work be completed?
A simpler version of the same type of problem is as follows:
2) A can do a piece of work in 14 days while B can do it in 21 days. They begin working together but 3 days before the completion of the work, A leaves off. The total number of days to complete the work is?
My attempt at problem 2:
A's 1 day work=1/14 and B's 1 day work= 1/21
Assume that it takes 'd' days to complete the entire work when both A and B are working together. Then,
(1/14 + 1/21)*d= 1
-> d=42/5 days.
But it is stated that 3 days before the completion of the work, A left. Therefore, work done by both in (d-3) days is:
(1/14 + 1/21)*(42/5 - 3)= 9/14
Remaining work= 1- 9/14 = 5/14 which is to be done by B alone. Hence the time taken by B to do (5/14) of the work is:
(5/14)*21 = 7.5 days.
Total time taken to complete the work = (d-3) + 7.5 = 12.9 days.
However, this answer does not concur with the one that is provided.
My Understanding of problem 1:
Problem 1 is an extended version of problem 2. But since i think i'm doing problem 2 wrong, following the same method on problem 1 will also result in a wrong answer.
Where did i go wrong?