Two towns, $X$ and $Y$, are connected by a straight road, $24$ miles long. Traveling from town $X$ to town $Y$, the speed limit changes every $6$ miles: from $30$ to $40$ to $50$ to $25$ miles per hour (mph). Two cars, one at town $X$ and one at town $Y$, 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 $X$, in miles, will the two cars meet?