Subjects algebra

Ratio Tables Cde533

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1. **Problem:** Complete the ratio tables for Water Tank and Swimming Pool, then analyze the ratios. 2. **Water Tank Table:** Given time (min) and liters leaked: - At 2 min: 4 liters - At 4 min: ? - At 6 min: ? - At 8 min: ? 3. **Swimming Pool Table:** Given time (min) and liters leaked: - At 3 min: 2 liters - At 6 min: ? - At 9 min: ? - At 12 min: ? 4. **Formula:** The ratio of liters leaked to time is constant if the leak rate is constant. Use the unit rate formula: $$\text{Rate} = \frac{\text{Liters leaked}}{\text{Time (min)}}$$ 5. **Water Tank Calculations:** - Rate at 2 min: $\frac{4}{2} = 2$ liters/min - At 4 min: $2 \times 4 = 8$ liters - At 6 min: $2 \times 6 = 12$ liters - At 8 min: $2 \times 8 = 16$ liters 6. **Swimming Pool Calculations:** - Rate at 3 min: $\frac{2}{3} \approx 0.6667$ liters/min - At 6 min: $0.6667 \times 6 = 4$ liters - At 9 min: $0.6667 \times 9 = 6$ liters - At 12 min: $0.6667 \times 12 = 8$ liters 7. **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 | 8. **Graphing:** Plot ordered pairs (time, liters leaked) for both tables. Water Tank points: (2,4), (4,8), (6,12), (8,16). Swimming Pool points: (3,2), (6,4), (9,6), (12,8). 9. **Conclusion:** Water Tank leaks at 2 liters/min, Swimming Pool leaks at approximately 0.6667 liters/min. Water Tank leaks faster.