Two towns, $R$ and $S$, are connected by a straight road, $18$ miles long. Traveling from town $R$ to town $S$, the speed limit changes every $9$ miles: from $36$ to $48$ miles per hour (mph). Two cars, one at town $R$ and one at town $S$, start moving toward each other at the same time. They drive at exactly the speed limit in each portion of the road. How far from town $R$, in miles, will the two cars meet?