Suppose that we have 2 cars parked in a line occupying spaces 1 and 2 of a parking lot. Spaces 3 and 4 are initially empty. Every minute, a car is considered eligible to move forward one space if a) the space in front of them is empty prior to any potential moves and b) label of the space they are on is less than 4. Suppose that every minute, if a car is eligible to move, it moves forward one space with probability 1/2. What is the expected amount of minutes before the cars occupy spaces 3 to 4?
Note: The space in front must be empty before any moves. For example, on the first turn, only the car in space 2 is eligible to move.