The problem involves a swimming pool being drained at a constant rate of 1515 gallons per minute, and it initially holds 1,200 gallons of water. We are tasked with finding an equation that represents the amount of water, $g$, left in the pool after $t$ minutes.

The key information is:

• Initial water: 1,200 gallons
• Drainage rate: 1,515 gallons per minute

Since the pool is being drained, the amount of water decreases as time $t$ increases, and the rate of change is constant at 1,515 gallons per minute.

Step-by-Step Process:

1. The initial amount of water in the pool is 1,200 gallons.
2. The pool loses 1,515 gallons per minute, so after $t$ minutes, the total amount of water lost is $1515 \times t$ gallons.
3. The remaining water $g$ after $t$ minutes is given by subtracting the total water lost from the initial amount.

Thus, the equation representing the amount of water left in the pool after $t$ minutes is:

$g = 1200 - 1515t$

This equation shows that as time $t$ increases, the amount of water $g$ decreases by 1,515 gallons for every minute.

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Would you like more details or have any questions about this problem? Here are some related questions you might find useful:

1. What happens if the drainage rate changes after a certain time?
2. How would the equation change if the pool was being filled instead of drained?
3. How long will it take to completely drain the pool?
4. What if the pool initially held more than 1,200 gallons of water?
5. How does this situation relate to linear functions in mathematics?

Tip: For problems involving constant rates of change, you can often model the situation using a linear equation.