A and B finish a job in 12 days, while A, B, and C finish in 8 days. How many days will C alone take?

This problem involves work and time, where individual work rates combine to determine collective completion time.

• Correct Answer: 24 days. If A and B finish a job in 12 days, their combined daily work rate is 1/12 of the job. If A, B, and C finish the job in 8 days, their combined daily work rate is 1/8 of the job. To find C's individual rate, subtract (A+B)'s rate from (A+B+C)'s rate: C's rate = 1/8 - 1/12. Finding a common denominator (24), this becomes 3/24 - 2/24 = 1/24. Thus, C alone completes 1/24 of the job per day, meaning C will take 24 days to finish the job.
• Distractors A, C, and D result from incorrect calculations or misapplication of the work-rate principle.

Understanding how to combine and subtract work rates is essential for these types of problems.