# RE3 | anthropic/claude-opus-5 | run 1

## Prompt

If 3 workers build a wall in 12 hours, how long would 4 workers take to build the same wall working at the same rate? Show your work.

## Response

Four workers would take **9 hours**. The work required is fixed at 36 worker-hours, so adding a fourth worker cuts the time proportionally.

## Step 1: Find the total work

Work is measured in worker-hours (the constant quantity here):

\[ W = 3 \text{ workers} \times 12 \text{ hours} = 36 \text{ worker-hours} \]

## Step 2: Divide by the new crew size

\[ t = \frac{36 \text{ worker-hours}}{4 \text{ workers}} = 9 \text{ hours} \]

## Step 3: Verify with the inverse proportion

Workers and time are inversely proportional, so \( n_1 t_1 = n_2 t_2 \):

\[ 3 \times 12 = 4 \times t_2 \implies t_2 = \frac{36}{4} = 9 \]

**Sanity check:** More workers means less time, and 9 hours is 3/4 of 12 hours — matching the ratio of 3 workers to 4 workers.

*Note:* This assumes perfect divisibility of labor with no coordination overhead or interference between workers, which real construction rarely achieves.

Want to try a variation, such as workers with different individual rates or a crew that changes size partway through the job?
