Working together, Sandy and Adrianna can design a website in 6 hours. If each works alone, Adrianna takes five more hours than it would take Sandy to do the same job. How long would it take Sandy to design a website working alone?
Working together, Sandy and Adrianna can design a website in 6 hours. If each works alone, Adrianna takes five more hours than it would take Sandy to do the same job. How long would it take Sandy to design a website working alone?
Chapter9: Quadratic Equations And Functions
Section9.5: Solve Applications Of Quadratic Equations
Problem 9.81TI: The weekly news magazine has a big story naming the Person of the Year and the editor wants the...
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![**Problem Statement for Educational Website**
*Collaborative Work Problem*
---
**Scenario:**
Working together, Sandy and Adrianna can design a website in 6 hours.
If each works alone, Adrianna takes five more hours than it would take Sandy to do the same job.
*Question:*
How long would it take Sandy to design a website working alone?
---
**Method to Solve:**
1. **Let \( t \) be the time (in hours) it takes Sandy to design a website alone.**
2. **Then, Adrianna's time to complete the same task would be \( t + 5 \) hours.**
3. **To find the combined work rate:**
- Sandy's work rate is \( \frac{1}{t} \) websites/hour.
- Adrianna's work rate is \( \frac{1}{t+5} \) websites/hour.
4. **Combined work rate when working together:**
- The combined rate is given by the sum of their individual rates: \( \frac{1}{t} + \frac{1}{t+5} \).
5. **Since working together they complete the website in 6 hours:**
- Combined work rate is also \( \frac{1}{6} \) websites/hour.
6. **Setting up the equation:**
\[
\frac{1}{t} + \frac{1}{t+5} = \frac{1}{6}
\]
7. **Solving the equation for \( t \) would give the time it takes Sandy to design a website alone.**
**Detailed Steps to Solve:**
1. **Find a common denominator and combine the fractions.**
2. **Set the equation equal to the combined work rate.**
3. **Solve for \( t \).**
This problem requires knowledge of algebra, especially working with rational equations to solve work problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70fe4f99-9e69-4bef-afe6-80d54e8903ee%2F1ff243b4-fdde-4070-8c98-5e5b7dcac7ab%2F24yixno_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement for Educational Website**
*Collaborative Work Problem*
---
**Scenario:**
Working together, Sandy and Adrianna can design a website in 6 hours.
If each works alone, Adrianna takes five more hours than it would take Sandy to do the same job.
*Question:*
How long would it take Sandy to design a website working alone?
---
**Method to Solve:**
1. **Let \( t \) be the time (in hours) it takes Sandy to design a website alone.**
2. **Then, Adrianna's time to complete the same task would be \( t + 5 \) hours.**
3. **To find the combined work rate:**
- Sandy's work rate is \( \frac{1}{t} \) websites/hour.
- Adrianna's work rate is \( \frac{1}{t+5} \) websites/hour.
4. **Combined work rate when working together:**
- The combined rate is given by the sum of their individual rates: \( \frac{1}{t} + \frac{1}{t+5} \).
5. **Since working together they complete the website in 6 hours:**
- Combined work rate is also \( \frac{1}{6} \) websites/hour.
6. **Setting up the equation:**
\[
\frac{1}{t} + \frac{1}{t+5} = \frac{1}{6}
\]
7. **Solving the equation for \( t \) would give the time it takes Sandy to design a website alone.**
**Detailed Steps to Solve:**
1. **Find a common denominator and combine the fractions.**
2. **Set the equation equal to the combined work rate.**
3. **Solve for \( t \).**
This problem requires knowledge of algebra, especially working with rational equations to solve work problems.
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