# RE3 | anthropic/claude-opus-5 | run 2

## 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

**9 hours.**

## Work

Total labor required is constant, so compute worker-hours:

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

Divide that fixed workload among 4 workers:

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

**Check via inverse proportion:** workers and time vary inversely, so \( t = 12 \times \frac{3}{4} = 9 \). Adding one worker (a 33% increase in labor) cuts the time by 25%.

*Note:* This assumes all workers work at identical rates with no interference or diminishing returns — a standard idealization in these problems, not always true on a real job site.

Want me to work through a variation, such as how many workers would be needed to finish in 4 hours?
