To find out how far Elena had run when she stopped, you need to calculate \( \frac{2}{3} \) of a mile.
To do this, multiply \( \frac{2}{3} \) by the total distance of 1 mile:
\[ \text{Distance run} = \frac{2}{3} \times 1 = \frac{2}{3} \text{ miles} \]
Thus, Elena had run \( \frac{2}{3} \) of a mile at that point.
The answer in simplest form is:
\[ \frac{2}{3} \text{ miles} \]