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The problem presented involves Max and his assistant painting a mural, where Max and his assistant start with different amounts of painted area and paint at different rates. The goal is to determine after how many hours both of them will have painted the same total area.

### Given Information:
- Max has already painted 12 square feet and paints 3 square feet per hour.
- Max's assistant has already painted 15 square feet and paints 2 square feet per hour.
- Let \( x \) represent the number of hours Max needs to paint so that he and his assistant will have painted the same amount of area.

### Step 1: Write an equation to represent the situation.
Max's painted area after \( x \) hours can be expressed as:
\[
\text{Max's area} = 12 + 3x
\]
Max's assistant's painted area after \( x \) hours is:
\[
\text{Assistant's area} = 15 + 2x
\]

We want to find when these two areas are equal, so we set the expressions equal to each other:
\[
12 + 3x = 15 + 2x
\]

### Step 2: Solve the equation.
\[
12 + 3x = 15 + 2x
\]
First, subtract \( 2x \) from both sides:
\[
12 + x = 15
\]
Next, subtract 12 from both sides:
\[
x = 3
\]

### Conclusion:
Max and his assistant will have painted the same area after 3 hours.

### Summary:
- The equation to represent the situation is \( 12 + 3x = 15 + 2x \).
- They will have painted the same area after 3 hours.

Would you like a more detailed explanation or do you have any questions?

Here are some related questions:
1. How would the equation change if Max's assistant painted 4 square feet per hour instead of 2?
2. What if Max had already painted 20 square feet at the start?
3. How would the result change if Max painted at 5 square feet per hour?
4. What would happen if both Max and his assistant started with the same initial area painted?
5. Can you find how much total area Max and his assistant will have painted together after 5 hours?

**Tip**: When solving equations, always perform the same operation on both sides to keep the equation balanced.

Max and his assistant are painting a mural. Max has already painted 12 square feet and can paint 3 square feet in an hour. Max's assistant already has 15 square feet painted and plans to paint 2 square feet per hour. After how many hours will they have painted the same area?

Learn how to solve a linear equation where Max and his assistant paint a mural at different rates. Max starts with 12 square feet and paints 3 square feet per hour, while his assistant starts with 15 square feet and paints 2 square feet per hour. This problem demonstrates how to find when they will have painted the same area. Suitable for Grades 6-8.

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