Let the distance of Sierra's morning walk be \( x \) miles. Therefore, her evening walk, being two and a half times as far, would be \( 2.5x \) miles.
Sierra walks Pepper twice a day, so the total distance walked in one day is:
\[ x + 2.5x = 3.5x \text{ miles} \]
Over the course of 7 days, the total distance she walks will be:
\[ 7 \times 3.5x = 24.5x \text{ miles} \]
According to the information given, her total walking distance over the week is 30 miles:
\[ 24.5x = 30 \]
To find \( x \), divide both sides by 24.5:
\[ x = \frac{30}{24.5} \approx 1.22449 \]
Thus, the distance of her morning walk is approximately \( 1.22 \) miles.
For simplicity, a more precise calculation gives:
\[ x \approx 1.2244898 \]
Thus, the answer to how long her morning walk is approximately:
\[ \boxed{1.22} \text{ miles} \]
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