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.