Actually, if they just wrote the code to update in real time how long it's taking the red card to get from the first post to the second, it would be constantly updating itself the whole time. Of course, they'd have to track multiple cards simultaneously, and update the wait time to the longest of the currently active cards...
They could put RFID receivers at both locations and automate the process so that the posted time is always accurate. Of course, even though it will then always be an accurate representation of how long the current boarder has waited in line, it still won't be a completely accurate measure of how long a person entering the line at that moment will wait.