Valeria has been training for the Charlestown Cruisers bike race. The first week she trained, she rode 5 days and took the same two routes each day. She rode an 8-mile route each morning and a longer route each evening. By the end of the week, she had ridden a total of 115 miles. How many miles did Valeria ride each evening?

Let's solve the problem step by step to determine how many miles Valeria rode each evening.

1. **Total miles Valeria rode in a week**: 115 miles.
2. **Number of days she trained**: 5 days.
3. **Miles rode each morning**: 8 miles (each morning).
4. **Miles rode each evening**: Let's denote this distance by \( x \) miles.

### Step-by-Step Solution:

**Step 1: Calculate the total distance Valeria rode in the mornings over the week.**

- Each morning, Valeria rode 8 miles.
- She rode for 5 days, so the total distance ridden in the morning is:
  \[
  5 \times 8 = 40 \text{ miles}
  \]

**Step 2: Determine the total distance ridden in the evenings over the week.**

- The total distance ridden in the week is 115 miles.
- Subtract the total morning distance from the total weekly distance to find the total distance ridden in the evenings:
  \[
  115 - 40 = 75 \text{ miles}
  \]

**Step 3: Calculate the distance ridden each evening.**

- Valeria rode in the evenings for 5 days, so:
  \[
  \frac{75}{5} = 15 \text{ miles per evening}
  \]

### Final Answer:
Valeria rode **15 miles** each evening.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. If Valeria increased her morning route to 10 miles each day, how many miles would she ride in the evenings to still reach 115 miles in a week?
2. If Valeria wants to ride a total of 130 miles in a week with the same morning routine, how many miles would she need to ride each evening?
3. How many miles would Valeria ride in total if she trained for 6 days instead of 5 with the same daily routine?
4. If Valeria decides to ride a longer morning route of 12 miles, how many miles would she need to ride each evening to still reach 115 miles in a week?
5. How many total miles would Valeria ride in a week if she doubled the length of her evening route?

**Tip:** When dealing with similar problems, always subtract the sum of the known quantities from the total to find the unknown quantity.

Learn how to calculate the distance Valeria rode each evening during her training week for the Charlestown Cruisers bike race. This problem involves basic arithmetic and equation-solving skills. Suitable for students in Grades 5-7.

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