1. **State the problem:** We need to find the length of a rectangular tank given its volume, width, and height. 2. **Formula:** The volume $V$ of a rectangular tank is given by: $$V = \text{length} \times \text{width} \times \text{height}$$ 3. **Given values:** - Volume $V = 350$ yd³ - Width $= 9 \frac{1}{3} = \frac{28}{3}$ yd - Height $= 3 \frac{1}{3} = \frac{10}{3}$ yd 4. **Find length:** Rearranging the formula to solve for length: $$\text{length} = \frac{V}{\text{width} \times \text{height}}$$ 5. **Calculate denominator:** $$\text{width} \times \text{height} = \frac{28}{3} \times \frac{10}{3} = \frac{280}{9}$$ 6. **Substitute values:** $$\text{length} = \frac{350}{\frac{280}{9}}$$ 7. **Simplify division by fraction:** $$\text{length} = 350 \times \frac{9}{280}$$ 8. **Simplify multiplication:** $$\text{length} = \frac{350 \times 9}{280} = \frac{3150}{280}$$ 9. **Simplify fraction by dividing numerator and denominator by 70:** $$\text{length} = \frac{\cancel{3150}^{45} \times 70}{\cancel{280}^{4} \times 70} = \frac{45}{4}$$ 10. **Convert improper fraction to mixed number:** $$\frac{45}{4} = 11 \frac{1}{4}$$ **Final answer:** The length of the tank is $11 \frac{1}{4}$ yards.