A pump fills a pool at a constant rate. At the end of 4 minutes, it has filled 1 gallon of water. Which table represents the relationship between the number of minutes and the numb... A pump fills a pool at a constant rate. At the end of 4 minutes, it has filled 1 gallon of water. Which table represents the relationship between the number of minutes and the number of gallons of water in the pool?
Understand the Problem
The question is asking which table correctly represents the relationship between time in minutes and the number of gallons of water filled in a pool, given that after 4 minutes, 1 gallon has been filled.
Answer
A
Answer for screen readers
The correct answer is A.
Steps to Solve
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Determine the rate of water filled per minute Since 1 gallon has been filled in 4 minutes, the rate of water filling can be calculated as: $$ \text{Rate} = \frac{1 \text{ gallon}}{4 \text{ minutes}} = 0.25 \text{ gallons per minute} $$
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Calculate water filled for given times in the tables For each table, calculate the expected gallons of water based on the time given in minutes using the rate:
- For 8 minutes: $$ 0.25 \times 8 = 2 \text{ gallons} $$
- For 12 minutes: $$ 0.25 \times 12 = 3 \text{ gallons} $$
- For 20 minutes: $$ 0.25 \times 20 = 5 \text{ gallons} $$
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Evaluate Table A for consistency The values in Table A (Time: 8, 12, 20; Water: 2, 3, 5) match the calculated values.
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Check Tables B, C, and D using the same method
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Table B:
- 8 minutes = 2 gallons (correct)
- 9 minutes: $$ 0.25 \times 9 = 2.25 \text{ gallons} $$ (incorrect)
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Table C:
- 4 minutes = 1 gallon (correct)
- 8 minutes = 2 gallons (incorrect)
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Table D:
- 4 minutes = 1 gallon (correct)
- 8 minutes: $$ 0.25 \times 8 = 2 \text{ gallons} $$ (incorrect)
- 12 minutes: $$ 0.25 \times 12 = 3 \text{ gallons} $$ (correct)
- Identify the correct table Only Table A correctly represents the relationship between time and gallons of water filled.
The correct answer is A.
More Information
Table A accurately reflects the constant filling rate of 0.25 gallons per minute, corresponding to the input of time. This ensures that the relationship described by the problem is met.
Tips
Some common mistakes include:
- Miscalculating the filling rate by not understanding the constant fill time.
- Incorrectly interpreting the time-gallon relationship by not applying the rate properly.
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