Subjects algebra

Leakage Rates 43Ef98

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We have two ratio tables showing the relationship between time (in minutes) and liters leaked for a Water Tank and a Swimming Pool. We need to complete the missing values in the tables and analyze the relationship. 2. **Water Tank table completion:** Given: - At 2 min, 4 liters leaked. Assuming the leak rate is constant, the ratio of liters leaked to time is constant. Formula: $$\text{Rate} = \frac{\text{Liters Leaked}}{\text{Time}}$$ Calculate rate: $$\frac{4}{2} = 2 \text{ liters per minute}$$ Use this rate to find missing values: - At 4 min: $$4 \times 2 = 8$$ liters - At 6 min: $$6 \times 2 = 12$$ liters - At 8 min: $$8 \times 2 = 16$$ liters 3. **Swimming Pool table completion:** Given: - At 3 min, 2 liters leaked. Calculate rate: $$\frac{2}{3} \approx 0.6667 \text{ liters per minute}$$ Use this rate to find missing values: - At 6 min: $$6 \times 0.6667 = 4$$ liters - At 9 min: $$9 \times 0.6667 = 6$$ liters - At 12 min: $$12 \times 0.6667 = 8$$ liters 4. **Conclusion:** Both tables show a constant rate of leakage, but the Water Tank leaks faster (2 liters/min) than the Swimming Pool (2/3 liters/min). The relationship between time and liters leaked is proportional in both cases. Final completed tables: Water Tank: | Time (min) | Liters Leaked | |------------|---------------| | 2 | 4 | | 4 | 8 | | 6 | 12 | | 8 | 16 | Swimming Pool: | Time (min) | Liters Leaked | |------------|---------------| | 3 | 2 | | 6 | 4 | | 9 | 6 | | 12 | 8 |