ray and peter csn psint s house in 15 hours when working together at the same time if ray works triple as fast as peter how long would it take peter to paint the house alone

Let's break down the problem:

- **Given:**
  - Ray and Peter can paint the house together in 15 hours.
  - Ray works three times as fast as Peter.

### Step 1: Define the work rates of Ray and Peter.
Let's assume:
- Peter's rate of work is \( x \) houses per hour.
- Ray's rate of work is \( 3x \) houses per hour (since Ray works three times as fast as Peter).

### Step 2: Determine their combined work rate.
- When working together, their combined work rate is the sum of their individual work rates:  
  \[
  x + 3x = 4x
  \]
  This means they can paint \( 4x \) houses per hour together.

### Step 3: Use the given time to find \( x \).
- Since they can paint the house together in 15 hours, the equation for their combined work rate is:
  \[
  4x \times 15 = 1 \text{ house}
  \]
  Simplifying:
  \[
  60x = 1
  \]
  \[
  x = \frac{1}{60}
  \]
  Therefore, Peter's rate is \( \frac{1}{60} \) houses per hour.

### Step 4: Determine how long it would take Peter to paint the house alone.
- To find the time it would take Peter to paint the house alone, use the formula:
  \[
  \text{Time} = \frac{\text{Total work}}{\text{Peter's rate}}
  \]
  Substituting the values:
  \[
  \text{Time} = \frac{1}{\frac{1}{60}} = 60 \text{ hours}
  \]

### Conclusion:
It would take Peter 60 hours to paint the house alone.

Would you like further details or have any questions? Here are some related questions for practice:

1. If Ray and Peter were to paint a second house, how long would it take them working together?
2. What would happen to the time if Ray worked at twice Peter's speed instead of three times?
3. How long would it take Ray alone to paint the house?
4. If Ray and Peter took a break for 5 hours, how would that affect their painting time?
5. What if a third person joined the work? How would the time change?

**Tip:** When dealing with work rate problems, always try to express everything in terms of a single variable to simplify the equations.

Learn how to calculate the time it would take Peter to paint a house alone when Ray works three times faster, based on their combined work rate. Detailed step-by-step solution included. Suitable for Grades 7-9.

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