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To solve this problem, let's determine the distance each student traveled along their respective routes:

1. **Route I**: The students who took Route I traveled along a path of \(6 \, \text{km} + 9 \, \text{km} = 15 \, \text{km}\).

2. **Route II**: The students who took Route II traveled along a path of \(3 \, \text{km} + 7 \, \text{km} + 6 \, \text{km} = 16 \, \text{km}\).

Now, we know:
- 2 students took Route I, so their total distance is \(2 \times 15 \, \text{km} = 30 \, \text{km}\).
- 3 students took Route II, so their total distance is \(3 \times 16 \, \text{km} = 48 \, \text{km}\).

**Total Distance Traveled by All Students**:
\[ 30 \, \text{km} + 48 \, \text{km} = 78 \, \text{km} \]

### Answer:
The total distance traveled by all students is **78 kilometers**.

Would you like a breakdown of the steps or any further details?

### Related Questions:
1. What if all students took the same route? How would that affect the total distance?
2. How would the total distance change if each route was reduced by 1 km?
3. If an additional student joined and took Route I, what would be the new total distance?
4. How can we represent this scenario with a function for any number of students taking each route?
5. How would the total distance differ if Route II was shortened to match Route I?

### Tip:
When dealing with multiple routes, it’s helpful to calculate each route's distance first before multiplying by the number of travelers.

2 students took Route I and 3 students took Route II to reach the end point. What is the total distance traveled by all students?

Determine the total distance traveled by all students as 2 students take Route I (15 km) and 3 students take Route II (16 km). This problem involves calculating distances using addition and multiplication, suitable for Grades 6-8.

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