Question
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?
Answers
GPT-4o mini
To understand the relationship between the number of minutes and the gallons of water in the pool, we first note the rate at which the pump fills the pool.
From the information given, the pump fills 1 gallon of water in 4 minutes. This means that the rate of filling is:
\[
\text{Rate} = \frac{1 \text{ gallon}}{4 \text{ minutes}} = 0.25 \text{ gallons per minute}
\]
Using this rate, we can calculate the amount of water filled for various times. Here’s how the relationship works:
- At 0 minutes, the pool has 0 gallons.
- At 1 minute, the pool has filled \(0.25 \times 1 = 0.25\) gallons.
- At 2 minutes, the pool has filled \(0.25 \times 2 = 0.5\) gallons.
- At 3 minutes, the pool has filled \(0.25 \times 3 = 0.75\) gallons.
- At 4 minutes, the pool has filled \(0.25 \times 4 = 1\) gallon.
- At 5 minutes, the pool has filled \(0.25 \times 5 = 1.25\) gallons.
- Continuing this pattern, at 6 minutes, it would be \(1.5\) gallons, and so on.
The points calculated are:
- (0, 0)
- (1, 0.25)
- (2, 0.5)
- (3, 0.75)
- (4, 1)
- (5, 1.25)
- (6, 1.5)
You could represent this data in a table format.
For example:
| Minutes | Gallons |
|---------|---------|
| 0 | 0 |
| 1 | 0.25 |
| 2 | 0.5 |
| 3 | 0.75 |
| 4 | 1 |
| 5 | 1.25 |
| 6 | 1.5 |
This table properly represents the linear relationship between the number of minutes and the number of gallons of water in the pool. If you have specific table options you would like evaluated, please provide them!
From the information given, the pump fills 1 gallon of water in 4 minutes. This means that the rate of filling is:
\[
\text{Rate} = \frac{1 \text{ gallon}}{4 \text{ minutes}} = 0.25 \text{ gallons per minute}
\]
Using this rate, we can calculate the amount of water filled for various times. Here’s how the relationship works:
- At 0 minutes, the pool has 0 gallons.
- At 1 minute, the pool has filled \(0.25 \times 1 = 0.25\) gallons.
- At 2 minutes, the pool has filled \(0.25 \times 2 = 0.5\) gallons.
- At 3 minutes, the pool has filled \(0.25 \times 3 = 0.75\) gallons.
- At 4 minutes, the pool has filled \(0.25 \times 4 = 1\) gallon.
- At 5 minutes, the pool has filled \(0.25 \times 5 = 1.25\) gallons.
- Continuing this pattern, at 6 minutes, it would be \(1.5\) gallons, and so on.
The points calculated are:
- (0, 0)
- (1, 0.25)
- (2, 0.5)
- (3, 0.75)
- (4, 1)
- (5, 1.25)
- (6, 1.5)
You could represent this data in a table format.
For example:
| Minutes | Gallons |
|---------|---------|
| 0 | 0 |
| 1 | 0.25 |
| 2 | 0.5 |
| 3 | 0.75 |
| 4 | 1 |
| 5 | 1.25 |
| 6 | 1.5 |
This table properly represents the linear relationship between the number of minutes and the number of gallons of water in the pool. If you have specific table options you would like evaluated, please provide them!