$\frac{3}{7}$th part of a bucket can be filled in one minute. Rest part of the bucket can be filled in:

Question

Accepted Answer

To solve the problem, we need to determine how long it will take to fill the rest of the bucket after $\frac{3}{7}$ of it is filled in one minute.

1. **Understanding the Problem:**
   - $\frac{3}{7}$ of the bucket is filled in 1 minute.
   - Therefore, the rate of filling is $\frac{3}{7}$ of the bucket per minute.

2. **Finding the Remaining Part:**
   - The remaining part of the bucket to be filled is $1 - \frac{3}{7} = \frac{4}{7}$.

3. **Calculating the Time to Fill the Remaining Part:**
   - Since $\frac{3}{7}$ of the bucket is filled in 1 minute, the time taken to fill $\frac{1}{7}$ of the bucket is $\frac{1}{\frac{3}{7}} = \frac{7}{3}$ minutes.
   - Therefore, the time to fill $\frac{4}{7}$ of the bucket is $\frac{4}{7} \times \frac{7}{3} = \frac{4}{3}$ minutes.

4. **Explanation of Why Option 4 is Correct:**
   - Option 4 states that the rest of the bucket can be filled in $\frac{4}{3}$ minutes, which matches our calculation. Therefore, Option 4 is the correct answer.

5. **Explanation of Why Other Options are Incorrect:**
   - **Option 1: $\frac{7}{3}$ minutes** - This option suggests that the entire bucket would take $\frac{7}{3}$ minutes to fill, which is incorrect because it only accounts for the time to fill $\frac{1}{7}$ of the bucket.
   - **Option 2: 21 minutes** - This option is incorrect because it suggests an excessively long time to fill the remaining $\frac{4}{7}$ of the bucket, which does not align with the filling rate.
   - **Option 3: $\frac{4}{7}$ minute** - This option is incorrect because it suggests that the remaining $\frac{4}{7}$ of the bucket can be filled in less than a minute, which contradicts the given rate of filling.

In conclusion, the correct answer is Option 4, $\frac{4}{3}$ minutes, as it accurately represents the time required to fill the remaining part of the bucket based on the given rate.