The Blue Lake Trail is \( 11 \frac{3}{8} \) miles long. Gemma has hiked \( 2 \frac{1}{2} \) miles each hour for 3 hours. How far is she from the end of the trail?

To find out how far Gemma is from the end of the trail, we first need to calculate the total distance she has hiked. Gemma hikes \( 2 \frac{1}{2} \) miles each hour for 3 hours, which is \( 2 \frac{1}{2} \times 3 \). Converting \( 2 \frac{1}{2} \) to an improper fraction gives us: \[ 2 \frac{1}{2} = \frac{5}{2} \] So, the total distance Gemma hiked is: \[ \frac{5}{2} \times 3 = \frac{15}{2} = 7 \frac{1}{2} \text{ miles} \] Now, let's subtract the distance she hiked from the total length of the trail: \[ 11 \frac{3}{8} - 7 \frac{1}{2} \] First, we convert both distances to improper fractions: \[ 11 \frac{3}{8} = \frac{11 \times 8 + 3}{8} = \frac{88 + 3}{8} = \frac{91}{8} \] \[ 7 \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2} = \frac{15 \times 4}{8} = \frac{60}{8} \] Now, we subtract the two fractions: \[ \frac{91}{8} - \frac{60}{8} = \frac{31}{8} \] Converting \( \frac{31}{8} \) back to a mixed number: \[ \frac{31}{8} = 3 \frac{7}{8} \] Thus, Gemma is \( 3 \frac{7}{8} \) miles from the end of the trail. So, the answer is \( 3 \frac{7}{8} \) miles!