### 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 ApproachThe 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### Calculations1. **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 ExplanationBelow 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}

given that Daryl and Cynthia both leave home at 7am for work heading opposite direction. 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

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

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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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}

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