Two cars sit in spaces 1 and 2 of a four-space row. Each minute a car with an empty space ahead moves forward with probability 1/2. How many minutes do you expect until they occupy spaces 3 and 4?

Two cars are parked in spaces 1 and 2 of a four-space row; spaces 3 and 4 are empty. Each minute, a car may move forward one space only if the space ahead was empty at the start of that minute and it is not already in space 4; each eligible car moves with probability 1/2. What is the expected number of minutes until the cars occupy spaces 3 and 4?