Subjects algebra

Rate Comparison

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1. **State the problem:** We need to find the rate at which Sebastian and Gabriel complete math problems per minute and then compare these rates to determine who works faster. 2. **Formula for rate:** Rate is calculated as $$\text{Rate} = \frac{\text{Number of problems}}{\text{Time in minutes}}$$ 3. **Calculate Sebastian's rate:** Sebastian completes 14 problems in 21 minutes. $$\text{Rate}_{Sebastian} = \frac{14}{21} = \frac{2}{3} \approx 0.6667 \text{ problems per minute}$$ 4. **Calculate Gabriel's rate:** Gabriel completes 36 problems in 1 hour. Since 1 hour = 60 minutes, $$\text{Rate}_{Gabriel} = \frac{36}{60} = 0.6 \text{ problems per minute}$$ 5. **Compare the rates:** Sebastian's rate is approximately 0.6667 problems per minute, and Gabriel's rate is 0.6 problems per minute. 6. **Conclusion:** Since $$0.6667 > 0.6$$, Sebastian completes problems more quickly than Gabriel. **Final answer:** Sebastian can complete problems more quickly.