# RE3 | perplexity/sonar-pro | 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

For this kind of question, you assume all workers work at the same constant rate and use **worker-hours** to keep the total amount of work the same. The answer is that 4 workers would take **9 hours** to build the same wall.

## Step-by-step solution

**1. Compute total work in worker-hours**

3 workers take 12 hours to build the wall.

Total work (in worker-hours) is:
\[
\text{Work} = \text{number of workers} \times \text{time} = 3 \times 12 = 36 \text{ worker-hours}
\]

This means it takes 36 worker-hours to build the wall.

**2. Use the same total work for 4 workers**

Let \( t \) be the time (in hours) for 4 workers to build the same wall.

Since the total work must still be 36 worker-hours:
\[
4 \times t = 36
\]

**3. Solve for \( t \)**

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

So, **4 workers would take 9 hours** to build the same wall, assuming all workers are equally productive and work at the same rate, and the wall size is unchanged.[Worker-hours method](https://askfilo.com/user-question-answers-smart-solutions/12-workers-take-9-hours-to-build-a-wall-then-6-workers-need-3231313830373132)

Would you like to see how to set this up using inverse proportion notation as well?
