While preparing to run a marathon, Amelia created a training schedule in which the distance of her longest run every week increased by a constant amount. If Amelia’s training schedule requires that her longest run in week 4 is a distance of 8 miles and her longest run in week 16 is a distance of 26 miles, which of the following best describes how the distance Amelia runs changes between week 4 and week 16 of her training schedule?

Options

A. A) Amelia increases the distance of her longest run by 0.5 miles each week.
B. B) Amelia increases the distance of her longest run by 2 miles each week.
C. C) Amelia increases the distance of her longest run by 2 miles every 3 weeks.
D. D) Amelia increases the distance of her longest run by 1.5 miles each week.

Explanation

To solve the problem, we need to determine how much Amelia increases her longest run each week between week 4 and week 16.

### Step-by-step Solution:

1. **Identify the distances for the given weeks**:
- In week 4, Amelia's longest run is 8 miles.
- In week 16, Amelia's longest run is 26 miles.

2. **Calculate the change in distance**:
- Change in distance = Distance in week 16 - Distance in week 4
- Change in distance = 26 miles - 8 miles = 18 miles.

3. **Calculate the change in weeks**:
- Change in weeks = Week 16 - Week 4
- Change in weeks = 16 - 4 = 12 weeks.

4. **Calculate the increase in distance per week**:
- Increase in distance per week = Change in distance / Change in weeks
- Increase in distance per week = 18 miles / 12 weeks = 1.5 miles per week.

5. **Conclusion**:
- Therefore, Amelia increases the distance of her longest run by 1.5 miles each week.

### Final Answer:
Amelia increases the distance of her longest run by **1.5 miles each week**.