Answer
$12$ miles
Work Step by Step
distance = (rate)$\times$(time) $\Rightarrow$ time = $\displaystyle \frac{\text{distance}}{\text{rate}}$
We are given:$\quad t_{2}=t_{1}+0.5$ (in hours),
where the indices 1 and 2 represent runners 1 and 2.
The time $t_{1}$ is shorter for the faster runner (runner 1)
Let d be the distance (length of the trail).
$\displaystyle \frac{d}{6}=\frac{d}{8}+\frac{1}{2}\qquad $.../$\times$LCD= 24
$4d=3d+12\qquad.../-3d$
$d=12$ miles
