Let's solve this step-by-step:

a) Volume of the pool in cubic feet:

The pool is shaped like a rectangular prism, so its volume can be found using the formula:

$V = \text{length} \times \text{width} \times \text{height}$

Given:

• Length = 6 feet
• Width = 4 feet
• Height = 2 feet

Substituting these values:

$V = 6 \times 4 \times 2 = 48 \, \text{cubic feet}$

So, the volume of the pool is 48 cubic feet.

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b) How many gallons of water will be needed to fill the pool?

We need to convert cubic feet to gallons. The conversion factor is:

$1 \, \text{cubic foot} = 7.48 \, \text{gallons}$

Now, multiplying the volume of the pool by the conversion factor:

$48 \, \text{cubic feet} \times 7.48 \, \text{gallons/cubic foot} = 359.04 \, \text{gallons}$

So, approximately 359 gallons of water will be needed to fill the pool.

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c) How long will it take to fill the pool?

We are given that the flow rate of a garden hose is between 9 and 17 gallons per minute. We'll use the average of these values:

$\text{Average flow rate} = \frac{9 + 17}{2} = 13 \, \text{gallons per minute}$

Now, we calculate the time required to fill the pool:

$\text{Time} = \frac{\text{Total gallons}}{\text{Flow rate}} = \frac{359 \, \text{gallons}}{13 \, \text{gallons per minute}} \approx 27.6 \, \text{minutes}$

Thus, it will take approximately 28 minutes to fill the pool.

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If you have any questions or need more details, feel free to ask!

Here are five related questions to expand the topic:

1. How would the time change if the flow rate of the hose was increased to 20 gallons per minute?
2. How many liters of water would the pool hold, given that 1 gallon = 3.785 liters?
3. What would happen if the pool's height was doubled—how would the volume and fill time change?
4. How much water would be needed if the pool was only filled to 75% of its capacity?
5. How long would it take to fill a smaller pool with dimensions 4 feet by 3 feet by 1.5 feet?

Tip: Always remember to check the units of measurement, especially when converting between systems (like feet to gallons or minutes to seconds). It ensures accurate results!