If six workers can complete a task in three days, how many days will two workers take to complete the same task, assuming constant productivity?

If six workers can complete a task in three days, how many days will two workers take to complete the same task, assuming constant productivity?

• A. 3
• B. 6
• C. 9
• D. 12

Answer: (C)

Work is spread evenly among the workers, and total output is proportional to the number of workers times the days worked. If six workers finish the task in three days, the total amount of work is 6 × 3 × (rate per worker per day). With only two workers, the days needed satisfy 2 × (days) × (rate per worker per day) = 6 × 3 × (rate per worker per day). The rate per worker cancels out, giving 2 × days = 18, so days = 9. So two workers would take nine days to complete the same task.

Work is spread evenly among the workers, and total output is proportional to the number of workers times the days worked. If six workers finish the task in three days, the total amount of work is 6 × 3 × (rate per worker per day). With only two workers, the days needed satisfy 2 × (days) × (rate per worker per day) = 6 × 3 × (rate per worker per day). The rate per worker cancels out, giving 2 × days = 18, so days = 9.

So two workers would take nine days to complete the same task.