To determine how long it takes to fill the pool, we need to follow these steps:

1. Calculate the volume of the pool in cubic feet: $\text{Volume} = \text{Width} \times \text{Length} \times \text{Depth}$ $\text{Volume} = 31 \, \text{ft} \times 47.6 \, \text{ft} \times 12.9 \, \text{ft} = 19035.72 \, \text{ft}^3$

2. Convert the volume from cubic feet to cubic inches: $1 \, \text{ft}^3 = 12^3 = 1728 \, \text{in}^3$ $\text{Volume in cubic inches} = 19035.72 \, \text{ft}^3 \times 1728 \, \text{in}^3/\text{ft}^3 = 32,895,569.6 \, \text{in}^3$

3. Convert the volume from cubic inches to gallons: $1 \, \text{gallon} = 231 \, \text{in}^3$ $\text{Volume in gallons} = \frac{32,895,569.6 \, \text{in}^3}{231 \, \text{in}^3/\text{gallon}} = 142,384 \, \text{gallons}$

4. Determine the time required to fill the pool: $\text{Time} = \frac{\text{Volume in gallons}}{\text{Flow rate}} = \frac{142,384 \, \text{gallons}}{12.8 \, \text{gal/min}} = 11,124.375 \, \text{min}$

Thus, it will take 11,124.375 minutes to fill the pool.

Would you like further details or have any questions?

Relative Questions:

1. How would the time change if the flow rate were doubled?
2. What if the pool's depth was reduced by 3 feet, how would it affect the filling time?
3. How much water (in gallons) would flow into the pool in 5 hours?
4. If the pool had a sloped bottom, how would you calculate the volume?
5. How many hours and minutes does 11,124.375 minutes convert to?

Tip: Always remember to keep track of units throughout calculations to avoid mistakes!