1. **State the problem:** She needs to mark a trail of length $1 \frac{3}{4}$ km, and she marks $\frac{3}{8}$ km every hour. We want to find how many hours it took to mark the whole trail. 2. **Convert mixed number to improper fraction:** $1 \frac{3}{4} = \frac{7}{4}$ km. 3. **Set up the equation:** Let $h$ be the number of hours. Since she marks $\frac{3}{8}$ km each hour, the total distance marked is $h \times \frac{3}{8}$ km. We want this to equal the total trail length: $$h \times \frac{3}{8} = \frac{7}{4}$$ 4. **Solve for $h$:** Multiply both sides by the reciprocal of $\frac{3}{8}$, which is $\frac{8}{3}$: $$h = \frac{7}{4} \times \frac{8}{3}$$ 5. **Simplify:** $$h = \frac{7 \times 8}{4 \times 3} = \frac{56}{12}$$ Divide numerator and denominator by 4: $$h = \frac{14}{3}$$ 6. **Convert to mixed number:** $$\frac{14}{3} = 4 \frac{2}{3}$$ hours. **Final answer:** It took $4 \frac{2}{3}$ hours to mark the whole trail.