Answer:
4 4/11 days
Explanation:
You want to know the remaining translation time after Ann works for 2 days, if Ann can do the job in 10 days while Ben can do it in 12 days, but Ann works alone for 2 days before they work together.
Ann's work
To find the amount of the job they need to finish the job, we can consider how much Ann gets done.
The rate each person works can be written in terms of job per day. That is the inverse of the given time as days per job.
Ann's rate: Ra = 1/10 jobs/day
Ben's rate: 1/12 jobs/day
Combined rate: Rb = (1/10 +1/12) = 22/120 = 11/60 jobs/day
The relationship between work done (quantity, Q), time (T) and rate (R) is ...
Q = RT or T = Q/R
The amount of work Ann did by herself is ...
Qa = RaTa = (1/10 job/day)(2 day) = 2/10 job = 1/5 job
Remaining work
Then the amount of work remaining is ...
Qb = 1 -1/5 = 4/5 job
Remaining time
The time it takes to do that working together is ...
Tb = Qb/Rb = (4/5 job)/(11/60 job/day) = 240/55 day = 4 4/11 days
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Additional comment
The attached calculator display shows the calculations we did.
Effectively, the combined rate of 11/60 job/day means the time for the job is 60/11 = 5 5/11 days/job when working together. 4/5 of the job will be (4/5 job)(5 5/11 days/job) = 4 4/11 days, as above.
It can be convenient to keep the units with the numbers. This can help you make sure the arithmetic you're doing is appropriate.