To find out how many miles Hilda will run in 3 hours, let's break down the problem step-by-step.
1. Determine the distance Hilda runs in half an hour:
Hilda runs [tex]\(\frac{2}{3}\)[/tex] of a mile in half an hour.
2. Convert 3 hours into the number of half-hour intervals:
There are [tex]\(2\)[/tex] half-hours in [tex]\(1\)[/tex] hour. Thus, in [tex]\(3\)[/tex] hours, there will be:
[tex]\[
3 \text{ hours} \times 2 = 6 \text{ half-hour intervals}
\][/tex]
3. Calculate the total distance Hilda will run in 3 hours:
Since she runs [tex]\(\frac{2}{3}\)[/tex] of a mile in each half-hour interval, we multiply the distance she runs in half an hour by the total number of half-hour intervals:
[tex]\[
\frac{2}{3} \text{ miles} \times 6 = 4 \text{ miles}
\][/tex]
Therefore, Hilda will run a total of [tex]\(4\)[/tex] miles in [tex]\(3\)[/tex] hours.
