At 9:30 am, Sean started filling a swimming pool. At 11:30 am, he had filled 1,800 gallons. If the pool has a capacity of 4,500 gallons, at what time will the pool be full?

To determine when the pool will be full, we first need to calculate the rate at which Sean fills the pool.

He started filling the pool at 9:30 am and filled 1,800 gallons by 11:30 am, which is a time span of 2 hours (from 9:30 am to 11:30 am).

The rate of filling can be calculated as follows:

\[
\text{Filling rate} = \frac{1,800 \text{ gallons}}{2 \text{ hours}} = 900 \text{ gallons per hour}
\]

Next, we need to find out how much more water is needed to fill the pool to its total capacity of 4,500 gallons:

\[
\text{Water needed} = 4,500 \text{ gallons} - 1,800 \text{ gallons} = 2,700 \text{ gallons}
\]

Now, we will calculate how long it will take to fill the remaining 2,700 gallons at the rate of 900 gallons per hour:

\[
\text{Time needed} = \frac{2,700 \text{ gallons}}{900 \text{ gallons per hour}} = 3 \text{ hours}
\]

Since Sean filled the pool until 11:30 am and it will take another 3 hours to fill the remaining amount, we calculate the end time:

\[
\text{End time} = 11:30 \text{ am} + 3 \text{ hours} = 2:30 \text{ pm}
\]

Therefore, the pool will be full at **2:30 pm**.