A variant of the PoleBarn Paradox
I'm having some trouble explaining the reasoning behind calling something a proper length. Here's the problem:
Bill is driving in a car, which he measures to have a length of 6m. Using his knowledge of special relativity, Bill is going to attempt an amazing stunt  he will park his car (temporarily, at least!) in a garage that is only 4m deep! To prove that he has successfully completed his stunt, Ted, who is standing by the garage, will carefully watch as Bill enters the garage, and close the front door of the garage when Bill's car is fully inside (the back door of the garage is closed already). Let Ted's reference frame be S and Bill's reference frame be S'.
a) Bill measures his car to have a length of 6m. Is this a proper length? Why or why not?
b) Ted measures the length of the garage to be 4m. Is this a proper length? Why or why not?
I know that they both are (probably), but I can not explain why. I know that Ted measured the length of the garage in a frame at rest, so it is a proper length, I'm having the most trouble with the car.
