Question 9 (2 points)

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Using ONLY your formula sheet, if water comes out of the garden hose at about 12 gallons per minute, how long will it take Eliza to fill this small pool half way?

Show your work and unit analysis HERE for full credit.  Include your answer with units and round to the nearest hundredth.

The computer will automatically mark this question incorrect and I will go back and give full credit if appropriate work is shown.

To solve this problem, we need to determine how long it will take to fill the pool halfway given the rate of water flow. Here’s how to approach it step-by-step:

### Step 1: Determine the volume of water needed
Let's assume the problem provides the total volume of the pool. For this example, I'll denote the total volume of the pool as \( V_{\text{pool}} \). Since we want to fill the pool halfway, the required volume of water is:
\[
V_{\text{required}} = \frac{1}{2} \times V_{\text{pool}}
\]

### Step 2: Convert the flow rate into the same units
The flow rate is given as 12 gallons per minute. This means that every minute, 12 gallons of water are added to the pool.

### Step 3: Calculate the time required to fill the pool halfway
The formula to calculate the time (\( t \)) to fill a volume at a given flow rate is:
\[
t = \frac{V_{\text{required}}}{\text{Flow rate}}
\]
Plugging in the known values:
\[
t = \frac{\frac{1}{2} \times V_{\text{pool}}}{12 \, \text{gallons per minute}}
\]

To simplify, we get:
\[
t = \frac{V_{\text{pool}}}{24} \, \text{minutes}
\]

### Step 4: Round to the nearest hundredth
The answer will depend on the given value of \( V_{\text{pool}} \). If you know the volume of the pool, substitute it into the formula to find the exact time and round your answer to the nearest hundredth.

### Example
If the total volume of the pool is 240 gallons, then:
\[
t = \frac{240}{24} = 10 \, \text{minutes}
\]

### Answer with Units:
For \( V_{\text{pool}} = 240 \) gallons, it will take **10.00 minutes** to fill the pool halfway.

Remember to replace \( V_{\text{pool}} \) with the actual value provided in your problem!

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Do you have the total volume of the pool, or would you like me to assume a different value? 

### Additional Questions for Practice:
1. If the flow rate changes to 15 gallons per minute, how would the time to fill the pool halfway change?
2. How would the answer change if the goal was to fill the pool three-quarters full?
3. What if the flow rate was in liters per minute? How would you convert and solve the problem?
4. If another pool has twice the volume of the current one, how long would it take to fill it halfway with the same flow rate?
5. How would the answer change if the hose was used intermittently, running only half of the time?

### Tip:
Always double-check the units used for both the flow rate and volume to ensure consistency in your calculations!

Using ONLY your formula sheet, if water comes out of the garden hose at about 12 gallons per minute, how long will it take Eliza to fill this small pool half way? Show your work and unit analysis HERE for full credit. Include your answer with units and round to the nearest hundredth.

Learn how to calculate the time it will take to fill a small pool halfway using a flow rate of 12 gallons per minute. This problem involves unit conversion and volume calculation and is suitable for students in Grades 6-8. Includes step-by-step explanation and formulas.

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