# RE3 | moonshotai/kimi-k3 | 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** to build the same wall. Since the number of workers and the time required are inversely proportional, the total amount of work stays constant regardless of how many workers are assigned.

## Step 1: Find the Total Work Required

The wall requires a fixed amount of labor, measured in worker-hours:

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

## Step 2: Divide by the New Number of Workers

Spread those 36 worker-hours across 4 workers:

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

## Verification

Using the inverse proportion relationship \( w_1 t_1 = w_2 t_2 \):

\[ 3 \times 12 = 4 \times 9 \implies 36 = 36 \checkmark \]

The answer checks out — adding one more worker reduces the time from 12 hours to 9 hours, a 25% decrease, which makes sense since the workforce grew by one-third.

Would you like to see how to handle a variation, such as workers with different individual rates?
