Answer:
23 days
Step-by-step explanation:
You want to know the total number of days required to make a batch of pens usually made by 12 machines in 20 days, when only 8 machines were used for the first 9 days.
The effort required for a batch of pens is ...
(20 days)(12 machines) = 240 machine·days
In the first 9 days, using only 8 machines, the effort used was ...
(9 days)(8 machines) = 72 machine·days
The remaining effort after those 9 days is ...
(240 -72) machine·days = 168 machine·days
When all 12 machines are available, the number of days required for that remaining effort is ...
[tex]\dfrac{168\text{ machine$\cdot$days}}{12\text{ machines}}=14\text{ days}[/tex]
Then the total time is ...
9 days + 14 days = 23 days
The total number of days taken to make the batch of pens is 23 days.
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Additional comment
We note that the 72 machine·days effort would usually be done in 72/12 = 6 days, instead of 9 days. That means the batch took 3 days, longer than normal, so the new total time is 20+3 = 23 days.