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.