Jill and her daughter run $2\frac{7}{8}$ miles in the morning and $1\frac{3}{4}$ miles in the evening every Sunday. We need to find the total distance they run each Sunday.

1. Problem Description

Jill and her daughter run $2\frac{7}{8}$ miles in the morning and $1\frac{3}{4}$ miles in the evening every Sunday. We need to find the total distance they run each Sunday.

2. Solution Steps

To find the total distance, we need to add the distances run in the morning and evening.

First, convert the mixed numbers to improper fractions:

$2\frac{7}{8} = \frac{2 \times 8 + 7}{8} = \frac{16+7}{8} = \frac{23}{8}$

$1\frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4+3}{4} = \frac{7}{4}$

Now, add the two improper fractions. To do this, we need a common denominator. The least common multiple of 8 and 4 is

8. Convert $\frac{7}{4}$ to an equivalent fraction with a denominator of 8:

$\frac{7}{4} = \frac{7 \times 2}{4 \times 2} = \frac{14}{8}$

Add the fractions:

$\frac{23}{8} + \frac{14}{8} = \frac{23+14}{8} = \frac{37}{8}$

Now, convert the improper fraction $\frac{37}{8}$ to a mixed number:

$\frac{37}{8} = 4\frac{5}{8}$ since $37 = 4 \times 8 + 5$.

3. Final Answer

$4\frac{5}{8}$