Let's work through the questions based on the data in the table.

The table shows how much water is in the pool after several minutes:

a) At what rate (in liters per minute) is the water flowing into the pool?

The rate at which water flows into the pool can be determined by finding the slope of the line that represents the relationship between time and the amount of water. The slope is:

$\text{Rate} = \frac{\Delta \text{Water}}{\Delta \text{Time}} = \frac{1500 - 375}{20 - 5} = \frac{1125}{15} = 75 \, \text{L/min}$

So, the water flows into the pool at a rate of 75 liters per minute.

b) How much water will be in the pool after 24 minutes? Show your calculations.

To calculate how much water will be in the pool after 24 minutes, we use the fact that the rate of water flow is constant (75 L/min). The equation for the amount of water as a function of time is:

$\text{Amount of Water} = \text{Rate} \times \text{Time}$

Substitute the known rate and the time of 24 minutes:

$\text{Amount of Water} = 75 \, \text{L/min} \times 24 \, \text{minutes} = 1800 \, \text{L}$

So, after 24 minutes, there will be 1800 liters of water in the pool.

c) If the pool has a capacity of 2125 L, approximately how many minutes (rounded to the nearest minute) will it take to fill the pool? Show your calculations.

We can find the time required to fill the pool by using the rate of 75 L/min. The equation is:

$\text{Time} = \frac{\text{Amount of Water}}{\text{Rate}} = \frac{2125 \, \text{L}}{75 \, \text{L/min}} \approx 28.33 \, \text{minutes}$

Rounding to the nearest minute, it will take approximately 28 minutes to fill the pool.

Would you like further explanations or details? Here are 5 additional questions to explore:

1. What assumptions are we making about the water flow in this scenario?
2. How would the answers change if the rate of water flow varied with time?
3. Can you derive a formula for the amount of water in the pool as a function of time?
4. How much time would it take to fill half of the pool's capacity?
5. If the rate were halved, how much time would it take to fill the pool?

Tip: When dealing with linear relationships, always look for patterns in the data such as consistent changes in time or amount.