1. **Stating the problem:** We need to find the total hours $h$ required to fill a swimming pool. 2. **Understanding the rates:** The problem gives two rates: one filling rate is $\frac{15}{4}$ pools per hour, and another is $\frac{1}{5}$ pools per hour. The number 1 likely represents the whole pool to be filled. 3. **Formula used:** When two rates work together, their combined rate is the sum of individual rates: $$\text{Combined rate} = \frac{15}{4} + \frac{1}{5}$$ 4. **Calculate the combined rate:** Find a common denominator for $\frac{15}{4}$ and $\frac{1}{5}$, which is 20. $$\frac{15}{4} = \frac{15 \times 5}{4 \times 5} = \frac{75}{20}$$ $$\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}$$ Add them: $$\frac{75}{20} + \frac{4}{20} = \frac{79}{20}$$ pools per hour. 5. **Find total time $h$:** Since the combined rate fills $\frac{79}{20}$ pools in 1 hour, the time to fill 1 pool is the reciprocal: $$h = \frac{1}{\frac{79}{20}} = \frac{20}{79}$$ hours. 6. **Final answer:** The pool will be filled in $$\boxed{\frac{20}{79}}$$ hours, approximately 0.253 hours or about 15.2 minutes.