1. **Problem statement:** A group of 12 people have enough water to last 9 days. (a) If 6 more people join, how long will the water last? (b) State one assumption made. 2. **Step 1: Understand the problem** The total amount of water is fixed and sufficient for 12 people for 9 days. 3. **Step 2: Calculate total person-days of water available** Total person-days = number of people $ \times $ number of days = $$12 \times 9 = 108$$ person-days. 4. **Step 3: New group size** New number of people = $$12 + 6 = 18$$. 5. **Step 4: Calculate how long water lasts for 18 people** Let the new number of days be $$d$$. Since total water is the same, person-days remain 108: $$18 \times d = 108$$ Solve for $$d$$: $$d = \frac{108}{18} = 6$$ days. 6. **Step 5: State the assumption** We assume that each person consumes water at the same constant rate every day. **Final answers:** (a) The water will last $$6$$ days for 18 people. (b) Assumption: Each person uses water at the same constant rate.