SOLUTION: Anna can do a piece of work in 12 days. Beth can do the same work in 15 days. Charles can also do the same piece of work in 30 days. Anna starts the work and Beth joins her after 3

Question 1157110: Anna can do a piece of work in 12 days. Beth can do the same work in 15 days. Charles can also do the same piece of work in 30 days. Anna starts the work and Beth joins her after 3 days. 3 days before the work is completed Anna leaves and Charles joins the work. In how many days will the work be completed?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You are given their rates of working:
Anna: [ 1 job ] / [ 12 days ]
Beth: [ 1 job ] / [ 15 days ]
Charles [ 1 job ] / [ 30 days ]
------------------------------------
Anna starts working alone and
works for 3 days. In 3 days she
does this fraction of the job:

There is of the job left
-------------------------------------
Anna and Beth then work together for
an unknown number of days.
Let = the number of days they work together
Their rate of working together is:

The fraction of the remaining work they get done is:

So now is done
is
the fraction left to do
---------------------------
Now for 3 days, Charles and Beth work together
and they finish the job
Add their rates of working

Multiply both sides by

So Anna and Beth worked together for days
------------------------------
Add up the days they all worked:
Anna alone: 3 days
Anna & Beth: 4 days
Charles and Beth: 3 days

They finish the work in 10 days
------------------------------------
Check my math and get a 2nd opinion if needed

Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!

Anna can do a piece of work in 12 days. Beth can do the same work in 15 days. Charles can also do the same piece of work in 30 days. Anna starts the work and Beth joins her after 3 days. 3 days before the work is completed Anna leaves and Charles joins the work. In how many days will the work be completed?

Anna can do the work in 12 days, or of work in 1 day Beth can do the work in 15 days, or of work in 1 day Charles can do the work in 30 days, or of work in 1 day We already know that Anna worked 3 days, alone, and that Beth and Charles worked 3 days, together. Therefore, we just need to know how many days Anna and Beth worked together. Let number of days Anna and Beth worked together, be T We then get: 15 + 5T + 4T + 12 + 6 = 60 -------- Multiplying by LCD, 60 5T + 4T + 15 + 12 + 6 = 60 9T + 33 = 60 9T = 27 Time Anna and Beth worked together, or Days needed to complete job: That’s ALL!! You can do the check, and if you do, you'll see that the entire job takes 9 days, not 10 as the other person states. Plus, his method is very time-consuming and complex - doesn't have to be - and most likely contain errors.

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