Question: Hello:

I need some assistance with the following:

Worker A can do a piece of work in 15 days, worker B in 12 days, and worker C in 10 days. Worker A works 2 days, worker B 3 days, and worker C 3 days. In what time can worker A and worker B finish the job by working together?

I think that the answer is 2 1/9 days.

This is a far as I got by trying to determine the answer:

Worker A 2/15
Worker B 3/12
Worker C 3/10

I added the fractions 240/1800 = 450/1800 + 540/1800 = 1230/1800
Now, I am unsure as to what to do next. Can someone provide me with some advice and assistance?

I thank you for any help that may be provided.

Kenneth,

I agree with you work so far. 1230/1800 = 41/60 so together they have completed forty-one sixtieth of the job and hence the proportion of the job they have left is

1 - 41/60 = 19/60.

Workers A and B together work at the rate of

2/15 + 3/12 = 23/60 of the job per day,

or said another way

60/21 days per job.

60/21 is approximately 3 so it takes them together almost 3 days to complete the job. But they don't have the entire job to complete, only 19/60 of the job and hence it will take them

60/21 19/60 = 19/21 days.

Penny