4 painters complete a painting job in 12 hours. How many painters are needed to complete the same job in 8 hours? What type of problem is it? Fluency, understanding, reasoning or problem solving.

This is a **work-rate problem** involving proportional reasoning. Here's the solution step-by-step:  

### Step 1: Define the relationship  
If 4 painters can complete the job in 12 hours, the total amount of **work done** is represented by:  
- \( W = \text{number of painters} \times \text{hours worked} = 4 \times 12 = 48 \text{ painter-hours} \).  
This means that 48 painter-hours are required to finish the job.

### Step 2: Set up the equation  
Now, if the job must be completed in 8 hours, let \( x \) be the number of painters required. Each of them will work for 8 hours. The total work will still need to be 48 painter-hours:  

\[
x \times 8 = 48
\]

### Step 3: Solve for \( x \)  
\[
x = \frac{48}{8} = 6
\]

So, **6 painters** are required to complete the job in 8 hours.

### What type of problem is this?  
This problem falls under **reasoning** because it involves analyzing the relationship between time, workers, and the amount of work. Specifically, it requires proportional thinking to understand how the number of workers and time are inversely related.

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Do you want further details or have any questions?  
Here are 5 related questions to explore:  
1. How long would it take for 2 painters to complete the same job?  
2. If 3 painters worked 6 hours each, what fraction of the job would be completed?  
3. What happens to the time if you double the number of painters?  
4. How would the solution change if one of the painters took a break halfway through?  
5. How does this problem relate to the concept of **inverse proportionality**?  

**Tip:** In work-rate problems, if the amount of work stays constant, increasing the number of workers decreases the required time proportionally.

4 painters complete a painting job in 12 hours. How many painters are needed to complete the same job in 8 hours? What type of problem is it? Fluency, understanding, reasoning, or problem solving.

Solve a work-rate problem: if 4 painters finish a job in 12 hours, determine the number of painters needed to complete the job in 8 hours. This problem uses concepts of proportional reasoning and inverse relationships between time and workers. Ideal for students in Grades 6-8.

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