To solve this problem, we need to determine the rates at which water flows into both containers and then compare these rates.
### Step-by-Step Solution
1. Determine the rate of flow for Container A:
- The rate at which water flows into Container A is given directly by the equation [tex]\( y = 17x \)[/tex]. This means that water flows into Container A at a constant rate of 17 gallons per hour.
2. Determine the rate of flow for Container B:
- It is given that after 8 hours, there are 152 gallons of water in Container B.
- To find the rate of flow into Container B, we use the formula: [tex]\[ \text{Rate} = \frac{\text{Total amount of water}}{\text{Time}} \][/tex]
- Thus, the rate for Container B is calculated as:
[tex]\[ \text{Rate of B} = \frac{152 \text{ gallons}}{8 \text{ hours}} = 19 \text{ gallons per hour} \][/tex]
3. Compare the rates:
- The rate of flow into Container A is 17 gallons per hour.
- The rate of flow into Container B is 19 gallons per hour.
4. Find the difference between the rates:
- Difference in rates = [tex]\(\text{Rate of B} - \text{Rate of A} \)[/tex]
- Difference = [tex]\(19 \text{ gallons per hour} - 17 \text{ gallons per hour} = 2 \text{ gallons per hour} \)[/tex]
5. Interpret the result:
- Since the rate of flow into Container B (19 gallons per hour) is greater than the rate of flow into Container A (17 gallons per hour) by 2 gallons per hour, it means that:
- Water flows into Container A at a rate 2 gallons per hour slower than Container B.
Based on the above steps, the correct statement is:
(B) Water flows into Container A at a rate 2 gallons per hour slower than Container B.
