To solve these problems, we need to determine the volume of each pool in cubic feet, convert it to gallons, and then use the rate of water flow from the hose to figure out how long it will take to fill each pool.

Step 1: Calculate the rate of water flow

You know that it takes 17 seconds to fill a 2-gallon watering can, so we can calculate the rate of water flow in gallons per second:

$\text{Flow rate} = \frac{2 \text{ gallons}}{17 \text{ seconds}} \approx 0.118 \text{ gallons per second}$

Step 2: Part a - Rectangular pool

The dimensions of the rectangular pool are 3 feet wide, 10 feet long, and 1 foot deep. The volume of the pool in cubic feet is given by:

$\text{Volume} = \text{width} \times \text{length} \times \text{depth} = 3 \times 10 \times 1 = 30 \text{ cubic feet}$

Now, convert this volume into gallons using the given conversion factor (1 cubic foot = 7.48 gallons):

$\text{Volume in gallons} = 30 \times 7.48 = 224.4 \text{ gallons}$

Step 3: Time to fill the rectangular pool

Using the flow rate (0.118 gallons per second), the time required to fill the pool is:

$\text{Time} = \frac{224.4 \text{ gallons}}{0.118 \text{ gallons per second}} \approx 1901 \text{ seconds}$

Convert this into minutes:

$\text{Time in minutes} = \frac{1901}{60} \approx 31.7 \text{ minutes}$

Step 4: Part b - Circular pool

The diameter of the circular pool is 13 feet, and the depth is 1 foot. The volume of a circular pool is given by the formula for the volume of a cylinder:

$\text{Volume} = \pi r^2 h$

Where:

• $r$ is the radius (half of the diameter, so $13/2 = 6.5$ feet),
• $h$ is the depth (1 foot).

Substitute the values:

$\text{Volume} = \pi (6.5)^2 \times 1 \approx 132.73 \text{ cubic feet}$

Convert this volume into gallons:

$\text{Volume in gallons} = 132.73 \times 7.48 \approx 992.8 \text{ gallons}$

Step 5: Time to fill the circular pool

Using the same flow rate (0.118 gallons per second), the time to fill the pool is:

$\text{Time} = \frac{992.8 \text{ gallons}}{0.118 \text{ gallons per second}} \approx 8413 \text{ seconds}$

Convert this into minutes:

$\text{Time in minutes} = \frac{8413}{60} \approx 140.2 \text{ minutes}$

Final Answers:

a. It will take approximately 31.7 minutes to fill the rectangular pool.
b. It will take approximately 140.2 minutes to fill the circular pool.

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Would you like more details or have any questions?

Follow-up questions:

1. What is the rate in gallons per minute for the hose?
2. How would the time change if the diameter of the circular pool increased to 15 feet?
3. How long would it take to fill half of the rectangular pool?
4. What would happen if the hose flow rate decreased to 1 gallon per 17 seconds?
5. How would the time change if the rectangular pool was only 0.5 feet deep?

Tip: For circular objects, always remember to use the formula for the volume of a cylinder when calculating the amount of water they hold.