Water flows into a swimming pool at the rate
of 12.8 gal/min.
If the pool dimensions are 31 ft wide, 47.6 ft
long and 12.9 ft deep, how long does it take to
fill the pool? (1 gallon = 231 cubic inches)
Answer in units of min.

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!

Learn how to calculate the time required to fill a swimming pool with dimensions 31 ft wide, 47.6 ft long, and 12.9 ft deep at a flow rate of 12.8 gallons per minute. Understand the conversion process from cubic feet to gallons and the application of unit conversion formulas. Suitable for students and enthusiasts of geometry and unit conversion.

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