Polyas problem solving.        A painter needs to paint fence that is 100 feet long. He can paint 10 feet per hour. How many hours will it take him to paint the entire fence? 

Let's break down the problem using **Polya's four-step problem-solving method**:

### 1. **Understand the problem**:
- **What is known?**
  - The fence is 100 feet long.
  - The painter paints 10 feet per hour.
  
- **What is being asked?**
  - How many hours will it take to paint the entire fence?

### 2. **Devise a plan**:
- To find the time, we can use the formula:
  \[
  \text{Time} = \frac{\text{Total distance (length of the fence)}}{\text{Rate (feet per hour)}}
  \]
  - In this case, the total distance is 100 feet, and the rate is 10 feet per hour.

### 3. **Carry out the plan**:
- Substituting the values into the formula:
  \[
  \text{Time} = \frac{100 \text{ feet}}{10 \text{ feet per hour}} = 10 \text{ hours}
  \]

### 4. **Look back**:
- The calculation is straightforward and makes sense. It will take the painter 10 hours to paint the entire fence.

### Final Answer:
It will take the painter **10 hours** to paint the entire fence.

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. If the painter increases his speed to 15 feet per hour, how long will it take him to finish the job?
2. What if the fence was 150 feet long? How many hours would he need then?
3. How would the time change if the painter took a break of 1 hour after every 2 hours of work?
4. If two painters work together, each painting 10 feet per hour, how long would it take them to finish the fence?
5. How many square feet would the painter cover if the height of the fence was 6 feet?

**Tip**: When solving problems, always look for simple, known formulas that relate the variables involved, like rate, distance, and time.

A painter needs to paint a fence that is 100 feet long. He can paint 10 feet per hour. How many hours will it take him to paint the entire fence?

Learn how to calculate the time it takes for a painter to paint a 100-foot fence when painting at a rate of 10 feet per hour. This basic arithmetic problem is suitable for students in Grades 5-6 and focuses on the relationship between rate, time, and distance.

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