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 prism is given by $$V = \text{length} \times \text{width} \times \text{height}$$ 3. **Given values:** - Volume $V = 525$ ft³ - Width $= 16 \frac{2}{3} = \frac{50}{3}$ ft - Height $= 2 \frac{4}{5} = \frac{14}{5}$ ft 4. **Find length:** Rearranging the formula, $$\text{length} = \frac{V}{\text{width} \times \text{height}}$$ 5. **Calculate denominator:** $$\text{width} \times \text{height} = \frac{50}{3} \times \frac{14}{5} = \frac{50 \times 14}{3 \times 5} = \frac{700}{15}$$ 6. **Simplify denominator:** $$\frac{700}{15} = \frac{\cancel{700}^{\times 7} \times 100}{\cancel{15}^{\times 3} \times 5} = \frac{140}{3}$$ 7. **Calculate length:** $$\text{length} = \frac{525}{\frac{140}{3}} = 525 \times \frac{3}{140}$$ 8. **Simplify multiplication:** $$525 \times \frac{3}{140} = \frac{525 \times 3}{140}$$ 9. **Simplify numerator and denominator:** $$\frac{\cancel{525}^{\times 3} \times 175}{\cancel{140}^{\times 4} \times 35} = \frac{175 \times 3}{35}$$ 10. **Further simplify:** $$\frac{175 \times 3}{35} = 5 \times 3 = 15$$ **Final answer:** $$\boxed{15}$$ ft