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?
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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!