1. **State the problem:** A racer jogged $5 \frac{3}{5}$ kilometers in $\frac{7}{8}$ hours. We need to find his average speed in kilometers per hour. 2. **Formula:** Average speed is given by the formula: $$\text{Average speed} = \frac{\text{Distance}}{\text{Time}}$$ 3. **Convert mixed number to improper fraction:** $5 \frac{3}{5} = \frac{5 \times 5 + 3}{5} = \frac{25 + 3}{5} = \frac{28}{5}$ kilometers. 4. **Calculate average speed:** $$\text{Average speed} = \frac{\frac{28}{5}}{\frac{7}{8}}$$ 5. **Divide fractions by multiplying by the reciprocal:** $$= \frac{28}{5} \times \frac{8}{7}$$ 6. **Simplify before multiplying:** $$= \frac{\cancel{28}^{4} \times \cancel{8}^{8}}{\cancel{5} \times \cancel{7}^{1}} = \frac{4 \times 8}{5 \times 1} = \frac{32}{5}$$ 7. **Convert to decimal:** $$\frac{32}{5} = 6.4$$ **Final answer:** The racer's average speed was $6.4$ kilometers per hour.