Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
Bartleby Related Questions Icon

Related questions

bartleby

Concept explainers

Question
100%
### 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
expand button
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
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Text book image
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Text book image
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
Text book image
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education