Numbers 19 discusses administering of the Red Heifer's ashes by way of sprinkling water. From verses 11 through 21, it seems that impurity contracted by the dead is dispelled by sprinklings on the third and seventh day from the time of being impure.
In the desert, this was certainly feasible, as all of Israel camped together. However, how was this done once the land was settled? Verse 9 seems to indicate that the ashes were stored in one place. Did people travel all the way to where the ashes were kept? Did they bring any impure vessels with them as well? Seems like quite a shlep, especially in the wake of a death in the family.