10) Daryl and Cynthia leave home at 7 am, heading in opposite directions for work. Cynthia usually spends 20 minutes biking to work while Daryl needs only 30 minutes to walk to work. Cynthia's average speed is 3 miles per hour faster than Daryl's average speed. If they work 6 miles apart, what is the average speed, in miles per hour, for each person? Distance Rate Time Daryl Cynthia
10) Daryl and Cynthia leave home at 7 am, heading in opposite directions for work. Cynthia usually spends 20 minutes biking to work while Daryl needs only 30 minutes to walk to work. Cynthia's average speed is 3 miles per hour faster than Daryl's average speed. If they work 6 miles apart, what is the average speed, in miles per hour, for each person? Distance Rate Time Daryl Cynthia
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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![### Problem Statement
**10) Daryl and Cynthia leave home at 7 am, heading in opposite directions for work. Cynthia usually spends 20 minutes biking to work while Daryl needs only 30 minutes to walk to work. Cynthia's average speed is 3 miles per hour faster than Daryl's average speed. If they work 6 miles apart, what is the average speed, in miles per hour, for each person?**
### Solution Approach
The problem involves two individuals, Daryl and Cynthia, who travel in opposite directions to work. While Cynthia bikes, Daryl walks. We need to determine their average speeds given certain conditions.
To solve for their speeds, let's denote:
- \( D \) = Daryl's average speed (in miles per hour)
- \( C \) = Cynthia's average speed (in miles per hour)
### Given Data
- Cynthia's biking time to work: 20 minutes \(= \frac{1}{3} \) hour
- Daryl's walking time to work: 30 minutes \(= \frac{1}{2} \) hour
- Cynthia's speed is 3 miles per hour faster than Daryl's speed: \( C = D + 3 \)
- Total distance between their workplaces: 6 miles
### Calculations
1. **Finding Daryl's Distance and Rate:**
- Distance \( = D \times 0.5 \) (since time is in hours)
2. **Finding Cynthia's Distance and Rate:**
- Distance \( = C \times \frac{1}{3} \) (since time is in hours)
Since their distances should add up to 6 miles:
\[ \frac{D}{2} + \frac{(D+3)}{3} = 6 \]
Simplify to find the speeds.
### Table Explanation
Below is a table listing the distance, rate (average speed), and time for Daryl and Cynthia's commute:
| | Distance | Rate | Time |
|----|----------|--------|---------|
| Daryl | \( \frac{D}{2} \) | \( D \) | 0.5 hours |
| Cynthia | \( \frac{(D+3)}{3} \) | \( D + 3 \) | 0.333 hours |
1. **Distance Calculation:**
\[ \frac{D}{2}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F265296a1-da32-4f4b-bf09-d4ccbee1822d%2F1b929776-2c0b-4e78-b121-9878ab51f265%2Fsxy355q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**10) Daryl and Cynthia leave home at 7 am, heading in opposite directions for work. Cynthia usually spends 20 minutes biking to work while Daryl needs only 30 minutes to walk to work. Cynthia's average speed is 3 miles per hour faster than Daryl's average speed. If they work 6 miles apart, what is the average speed, in miles per hour, for each person?**
### Solution Approach
The problem involves two individuals, Daryl and Cynthia, who travel in opposite directions to work. While Cynthia bikes, Daryl walks. We need to determine their average speeds given certain conditions.
To solve for their speeds, let's denote:
- \( D \) = Daryl's average speed (in miles per hour)
- \( C \) = Cynthia's average speed (in miles per hour)
### Given Data
- Cynthia's biking time to work: 20 minutes \(= \frac{1}{3} \) hour
- Daryl's walking time to work: 30 minutes \(= \frac{1}{2} \) hour
- Cynthia's speed is 3 miles per hour faster than Daryl's speed: \( C = D + 3 \)
- Total distance between their workplaces: 6 miles
### Calculations
1. **Finding Daryl's Distance and Rate:**
- Distance \( = D \times 0.5 \) (since time is in hours)
2. **Finding Cynthia's Distance and Rate:**
- Distance \( = C \times \frac{1}{3} \) (since time is in hours)
Since their distances should add up to 6 miles:
\[ \frac{D}{2} + \frac{(D+3)}{3} = 6 \]
Simplify to find the speeds.
### Table Explanation
Below is a table listing the distance, rate (average speed), and time for Daryl and Cynthia's commute:
| | Distance | Rate | Time |
|----|----------|--------|---------|
| Daryl | \( \frac{D}{2} \) | \( D \) | 0.5 hours |
| Cynthia | \( \frac{(D+3)}{3} \) | \( D + 3 \) | 0.333 hours |
1. **Distance Calculation:**
\[ \frac{D}{2}
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