  We study traveling time and traveling length for tracer dispersion in porous
media. We model porous media by two-dimensional bond percolation, and we model
flow by tracer particles driven by a pressure difference between two points
separated by Euclidean distance $r$. We find that the minimal traveling time
$t_{min}$ scales as $t_{min} \sim r^{1.40}$, which is different from the
scaling of the most probable traveling time, ${\tilde t} \sim r^{1.64}$. We
also calculate the length of the path corresponding to the minimal traveling
time and find $\ell_{min} \sim r^{1.13}$ and that the most probable traveling
length scales as ${\tilde \ell} \sim r^{1.21}$. We present the relevant
distribution functions and scaling relations.
