# RE3 | meta/muse-spark-1.1 | 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

With 4 workers at the same rate, the wall would take **9 hours**. This is an inverse proportion — more workers means less time for the same amount of work.

## How to Solve It

**Step 1: Find the total amount of work**

Calculate the work in worker-hours:

\[ \text{Total Work} = \text{Number of Workers} \times \text{Time} \]
\[ \text{Total Work} = 3 \times 12 = 36 \text{ worker-hours} \]

**Step 2: Calculate the new time**

Divide the total work by the new number of workers:

\[ \text{Time}_2 = \frac{\text{Total Work}}{\text{Workers}_2} \]
\[ \text{Time}_2 = \frac{36}{4} = 9 \text{ hours} \]

You can also use the inverse proportion formula directly:

\[ T_2 = \frac{W_1 \times T_1}{W_2} = \frac{3 \times 12}{4} = 9 \]

So 4 workers working at the same rate would complete the same wall in 9 hours.

Want me to show you how to solve it if the workers have different rates?
