A garden hose fills ¾ of a bucket in 12 minutes how much is filled in 3 minutes

To solve this problem, we first need to find the rate at which the garden hose fills the bucket. Then, we can use that rate to determine how much of the bucket is filled in 3 minutes.

### Step 1: Find the Rate of Filling

We know that the garden hose fills \(\frac{3}{4}\) of a bucket in 12 minutes. To find the rate of filling, we can express this as:

\[
\text{Filling rate} = \frac{\text{Amount filled}}{\text{Time}}
\]

\[
\text{Filling rate} = \frac{\frac{3}{4} \text{ bucket}}{12 \text{ minutes}}
\]

To simplify this fraction, we divide \(\frac{3}{4}\) by 12:

\[
\text{Filling rate} = \frac{3}{4} \div 12 = \frac{3}{4} \times \frac{1}{12} = \frac{3}{48} = \frac{1}{16} \text{ buckets per minute}
\]

### Step 2: Calculate the Amount Filled in 3 Minutes

Now, we can use the filling rate to find out how much of the bucket is filled in 3 minutes:

\[
\text{Amount filled} = \text{Filling rate} \times \text{Time}
\]

\[
\text{Amount filled} = \frac{1}{16} \text{ buckets per minute} \times 3 \text{ minutes}
\]

\[
\text{Amount filled} = \frac{3}{16} \text{ buckets}
\]

### Conclusion

The garden hose fills \(\frac{3}{16}\) of a bucket in 3 minutes.

### Follow-up Questions:

1. How long will it take to fill the entire bucket at the same rate?
2. How much of the bucket is filled in 6 minutes?
3. If the bucket is doubled in size, how long will it take to fill the new bucket using the same hose?
4. How much of the bucket is filled in 1 minute?
5. If the hose fills 1 bucket in 16 minutes, how many buckets will it fill in 1 hour?

### Tip:

When working with rates, ensure you understand what the rate represents and always multiply the rate by the time to find the total quantity.

Learn how to calculate the amount filled by a garden hose in 3 minutes using proportional reasoning. This problem involves determining the rate of filling and applying it to find the amount of water filled in a specified time period. Suitable for students in Grades 5-7.

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