### Collaborative Work Calculation#### Problem Description:Hannah can paint a room in 15 hours. Destiny can paint the same room in 9 hours. How long does it take for both Hannah and Destiny to paint the room if they are working together?#### Solution:Step-by-Step Explanation:1. **Determine Each Person's Work Rate**: - Hannah's work rate: $ \frac{1 \text{ room}}{15 \text{ hours}} = \frac{1}{15} $ (rooms per hour) - Destiny's work rate: $ \frac{1 \text{ room}}{9 \text{ hours}} = \frac{1}{9} $ (rooms per hour)2. **Combine Their Work Rates**: - Combined work rate: $ \frac{1}{15} + \frac{1}{9} $3. **Find a Common Denominator for Adding Fractions**: - Common denominator for 15 and 9 is 45: \[ \frac{1}{15} = \frac{3}{45} \] \[ \frac{1}{9} = \frac{5}{45} \]4. **Add the Fractions**: - $ \frac{3}{45} + \frac{5}{45} = \frac{8}{45} $ (rooms per hour as a combined rate)5. **Determine Time by Taking the Reciprocal**: - Time taken: $ \frac{45}{8} $ hours6. **Simplify if Possible**: - $ \frac{45}{8} = 5.625 $ hoursTherefore, it will take both Hannah and Destiny approximately 5.625 hours to paint the room together.##### Input Box for Answer:[Input Box] hours

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Hannah can paint a room in 15 hours. Destiny can paint the same room in 9 hours. How long does it take for both Hannah and Destiny to paint the room it they are working together. hours

Algebra and Trigonometry (6th Edition)

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ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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### Collaborative Work Calculation

#### Problem Description:
Hannah can paint a room in 15 hours. Destiny can paint the same room in 9 hours. How long does it take for both Hannah and Destiny to paint the room if they are working together?

#### Solution:

Step-by-Step Explanation:
1. **Determine Each Person's Work Rate**:
- Hannah's work rate: $ \frac{1 \text{ room}}{15 \text{ hours}} = \frac{1}{15} $ (rooms per hour)
- Destiny's work rate: $ \frac{1 \text{ room}}{9 \text{ hours}} = \frac{1}{9} $ (rooms per hour)

2. **Combine Their Work Rates**:
- Combined work rate: $ \frac{1}{15} + \frac{1}{9} $

3. **Find a Common Denominator for Adding Fractions**:
- Common denominator for 15 and 9 is 45:
\[ \frac{1}{15} = \frac{3}{45} \]
\[ \frac{1}{9} = \frac{5}{45} \]

4. **Add the Fractions**:
- $ \frac{3}{45} + \frac{5}{45} = \frac{8}{45} $ (rooms per hour as a combined rate)

5. **Determine Time by Taking the Reciprocal**:
- Time taken: $ \frac{45}{8} $ hours

6. **Simplify if Possible**:
- $ \frac{45}{8} = 5.625 $ hours

Therefore, it will take both Hannah and Destiny approximately 5.625 hours to paint the room together.

##### Input Box for Answer:
[Input Box] hours

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