Cars advancing to the end

Two cars occupy spaces $1$ and $2$ of a $4$-space lot (spaces $3$, $4$ empty). Each minute, a car is eligible to advance one space if the space directly ahead is empty (before any moves that minute) and its current space number is $< 4$; each eligible car independently advances with probability $\tfrac12$. What is the expected number of minutes until the cars occupy spaces $3$ and $4$?