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Let's work through this problem step by step:

### Part (a):
We know that:
- The water supply is enough for **8 people** to last **9 days**.
- The question asks how long the water supply will last if **4 more people join**, making the total number of people **12**.

The total "person-days" the current water supply can cover is:
\[
8 \text{ people} \times 9 \text{ days} = 72 \text{ person-days}.
\]
Now, with 12 people, we want to know how long this water will last. Let \( x \) be the number of days the water will last with 12 people:
\[
12 \text{ people} \times x \text{ days} = 72 \text{ person-days}.
\]
Solving for \( x \):
\[
x = \frac{72}{12} = 6 \text{ days}.
\]
So, the water will last **6 days** if 4 more people join the group.

### Part (b):
One assumption made in part (a) is that **each person consumes water at the same rate**. That is, the water consumption per person per day remains constant regardless of the size of the group.

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Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How would the solution change if the new group members consume water at a different rate?
2. What would happen if the water supply increased but the number of people stayed the same?
3. How many days would the water last if only 2 more people joined the trek instead of 4?
4. If each person consumes 1.5 liters of water per day, how many liters of water are available for the group?
5. How much water does one person need for the entire 9-day trek?

**Tip**: When dealing with problems involving rates (like water consumption), always calculate the total "resource" available (such as person-days) before redistributing it across the new scenario.

A group of 8 people on a trek have enough water to last 9 days. If 4 more people join the trek, how long will the water supply last the whole group?

Explore how to calculate the duration of water supply for a group when the number of people increases. Learn about person-days, proportions, and assumptions on constant water consumption per person. Suitable for students in Grades 6-8.

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