I really enjoyed this! I always love the added wrinkle of "co-op" puzzle-solving, but usually it comes in the form of clones that share your controls or time clones or something similarly clumsy. I've never seen anything quite like this before and it was pretty interesting.
I think the physics might be tied to the draw framerate; I first tried it in my main browser (which has a zillion tabs open, so JavaScript can be a bit laggy), and the box moved almost unusably slowly. Seemed fine in a secondary browser.
It might've been nice if the exit doors were a different color or something; that confused me on the third puzzle, where the screen is so tall that a good chunk of the fourth puzzle gets included as well. You did a lot with very little graphics-wise here though; very nice :)