If 5 workers can complete a task in 8 days, how many days will it take 4 workers to complete the same task, assuming constant productivity?

If 5 workers can complete a task in 8 days, how many days will it take 4 workers to complete the same task, assuming constant productivity?

• A. 8 days
• B. 9 days
• C. 10 days
• D. 12 days

Answer: (C)

With constant productivity per worker, the total amount of work is fixed and equals the number of workers times the number of days worked, i.e., worker-days. Five workers in eight days use 5 × 8 = 40 worker-days of effort. The same 40 worker-days must be completed by four workers, so the time needed is 40 ÷ 4 = 10 days. You can also see this by scaling the time: reducing the crew from five to four increases the time by a factor of 5/4, so eight days × 5/4 = 10 days. Therefore, it will take ten days.

With constant productivity per worker, the total amount of work is fixed and equals the number of workers times the number of days worked, i.e., worker-days. Five workers in eight days use 5 × 8 = 40 worker-days of effort. The same 40 worker-days must be completed by four workers, so the time needed is 40 ÷ 4 = 10 days. You can also see this by scaling the time: reducing the crew from five to four increases the time by a factor of 5/4, so eight days × 5/4 = 10 days. Therefore, it will take ten days.