1. **State the problem:** We need to find how many weeks it takes to finish a quilt that is 3 1/4 meters long if 1/6 of a meter is completed each week. 2. **Convert mixed number to improper fraction:** $$3 \frac{1}{4} = \frac{13}{4}$$ meters. 3. **Use the formula:** $$\text{Number of weeks} = \frac{\text{Total length}}{\text{Length per week}}$$ 4. **Substitute values:** $$\text{Number of weeks} = \frac{\frac{13}{4}}{\frac{1}{6}}$$ 5. **Divide fractions by multiplying by the reciprocal:** $$\frac{13}{4} \times \frac{6}{1} = \frac{13 \times 6}{4} = \frac{78}{4}$$ 6. **Simplify the fraction:** $$\frac{78}{4} = 19 \frac{2}{4} = 19 \frac{1}{2}$$ weeks. 7. **Interpretation:** It takes 19 and a half weeks to finish the quilt at the rate of 1/6 meter per week.