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
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)
6th Edition
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88d18a19-21f4-41fb-afe0-306734676977%2F6231bfe6-d988-475b-a170-587ff46692d7%2Fds222vg.png&w=3840&q=75)
Transcribed Image Text:### 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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