Solve for Time: 3 Workers vs 4 Workers Painting Rate Problem

To solve this problem, we'll follow these steps:

• Step 1: Calculate the work rate for the 3 workers.
• Step 2: Determine the equivalent rate when 4 workers are involved.
• Step 3: Calculate the time required for 4 workers using the combined rate.

Let's go through each step in detail:

Step 1: Calculate the work rate for the 3 workers.
If 3 workers can complete the task in 4 hours, then their combined work rate is:

$\text{Rate of 3 workers} = \frac{1 \text{ room}}{4 \text{ hours}}$

Therefore, the rate of 1 worker is:

$\text{Rate of 1 worker} = \frac{1}{3} \times \frac{1 \text{ room}}{4 \text{ hours}} = \frac{1}{12} \text{ rooms per hour}$

Step 2: Determine the equivalent rate when 4 workers are involved.
If each worker has a rate of $\frac{1}{12} \text{ rooms per hour}$, then 4 workers would have a combined rate of:

$\text{Rate of 4 workers} = 4 \times \frac{1}{12} \text{ rooms per hour} = \frac{4}{12} \text{ rooms per hour} = \frac{1}{3} \text{ rooms per hour}$

Step 3: Calculate the time required for 4 workers using the combined rate.
To complete 1 room, the time required by 4 workers is:

$\text{Time} = \frac{\text{Work}}{\text{Rate}} = \frac{1 \text{ room}}{\frac{1}{3} \text{ rooms per hour}} = 3 \text{ hours}$

Therefore, the solution to the problem is 3 hours.