1. **Problem statement:** 6. b) If the school only has one pump, how long will it take to fill the pool? Given answer: 9.6 hrs. 6. c) Convert the answer from b) into days. 7.1) Complete the speed column in the table using the formula $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$. 7.2) Determine if the speed changes. 7.3) Predict based on the speed behavior. 7.4) State if distance is directly or indirectly proportional to time. 2. **Step 6. b)** The problem states the time is 9.6 hours for one pump to fill the pool, so the answer is: $$\boxed{9.6 \text{ hours}}$$ 3. **Step 6. c)** Convert 9.6 hours to days. We know: $$1 \text{ day} = 24 \text{ hours}$$ So, $$\text{Time in days} = \frac{9.6}{24}$$ Show canceling for simplification: $$\frac{\cancel{9.6}}{\cancel{24}} = 0.4$$ Therefore, $$\boxed{0.4 \text{ days}}$$ 4. **Step 7.1)** Calculate speed for each time-distance pair using $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$: - For 10 min and 21 km: $$\text{Speed} = \frac{21}{10} = 2.1 \text{ km/min}$$ - For 20 min and 42 km: $$\text{Speed} = \frac{42}{20} = 2.1 \text{ km/min}$$ - For 30 min and 63 km: $$\text{Speed} = \frac{63}{30} = 2.1 \text{ km/min}$$ - For 40 min and 84 km: $$\text{Speed} = \frac{84}{40} = 2.1 \text{ km/min}$$ - For 50 min and 105 km: $$\text{Speed} = \frac{105}{50} = 2.1 \text{ km/min}$$ All speeds are $2.1$ km/min. 5. **Step 7.2)** The speed changes at ________? Since all speeds are equal to $2.1$ km/min, the speed does not change. Answer: $$\boxed{\text{speed does not change}}$$ 6. **Step 7.3)** Because the car is travelling at a ________ speed we can predict ________? Since speed is constant, the car travels at a constant speed. We can predict the distance will increase linearly with time. Answer: $$\boxed{\text{constant speed; distance increases linearly with time}}$$ 7. **Step 7.4)** Distance is directly/indirectly proportional to time? Since speed is constant, distance is directly proportional to time. Answer: $$\boxed{\text{directly proportional}}$$