In 1 minute, \(\frac{3}{7}\) of a bucket is filled. The rest of the bucket can be filled in:

Given:

In 1 minute, \(\frac{3}{7}\) of a bucket is filled.

Formula Used:

Time to fill the rest of the bucket = (Fraction of the bucket to be filled) / (Rate of filling per minute)

Calculation:

Fraction of the bucket already filled = \(\frac{3}{7}\)

Fraction of the bucket remaining = 1 - \(\frac{3}{7}\)

⇒ Fraction remaining = \(\frac{7}{7} - \frac{3}{7}\)

⇒ Fraction remaining = \(\frac{4}{7}\)

Rate of filling per minute = \(\frac{3}{7}\) of the bucket per minute.

Time to fill the remaining part = \(\frac{\text{Fraction remaining}}{\text{Rate of filling per minute}}\)

⇒ Time = \(\frac{\frac{4}{7}}{\frac{3}{7}}\)

⇒ Time = \(\frac{4}{7} × \frac{7}{3}\)

⇒ Time = \(\frac{4}{3}\) minutes

The time to fill the rest of the bucket is \(\frac{4}{3}\) minutes.

The correct answer is option 3.