Yuna hikes a trail that is \( \frac{3}{5} \) miles long. She hikes \( \frac{5}{8} \) of the trail before she rests. How many more niles does Yuna hike to reach the end of the trail?

Yuna has already hiked \( \frac{5}{8} \) of the trail, which is \( \frac{3}{5} \) miles long. To find out how far she has hiked, we need to calculate: \[ \text{Distance hiked} = \frac{5}{8} \times \frac{3}{5} = \frac{15}{40} = \frac{3}{8} \text{ miles.} \] Next, we determine how much distance remains to hike. The total length of the trail is \( \frac{3}{5} \) miles, and Yuna has hiked \( \frac{3}{8} \) miles, so: \[ \text{Remaining distance} = \frac{3}{5} - \frac{3}{8}. \] To do this subtraction, we need a common denominator, which is 40: \[ \frac{3}{5} = \frac{24}{40} \quad \text{and} \quad \frac{3}{8} = \frac{15}{40}. \] Now, we can subtract: \[ \frac{24}{40} - \frac{15}{40} = \frac{9}{40}. \] So Yuna has \( \frac{9}{40} \) miles left to hike to reach the end of the trail.