Three workers can paint a fence in 4 days. If one more worker joins the team, how many days will it take them to finish the work? What are the assumptions you need to make?
Given: 3 workers can paint a fence in 4 days. One more worker joins the team.
Formula: Workers × Days = Constant work (inverse proportion)
Calculation: Step 1: Total work = 3 workers × 4 days = 12 worker-days Step 2: New number of workers = 3 + 1 = 4 workers Step 3: New time = 12 worker-days ÷ 4 workers = 3 days
Answer: It will take 3 days to finish the work.
Assumptions: (1) All workers work at the same rate. (2) The work is divided equally among all workers.
Explanation
The chapter demonstrates inverse proportion with worker-day problems. Workers × Days = Constant work. Initial: = 12 worker-days. New workers = 3 + 1 = 4. Days = 12 ÷ 4 = 3 days.
Solution Steps
Step 1: Calculate total work in worker-days: 3 workers × 4 days = 12 worker-days
Step 2: Find new number of workers: 3 + 1 = 4 workers
Step 3: Calculate new time: 12 worker-days ÷ 4 workers = 3 days