Playa del carmen / cozumel ferry?

My family and I are going to Cozumel for vacation this winter. We really want to explore on the mainland too though; and i saw that the car ferry takes 4-5 hours. does anyone think its possible to rent a car in cancun, leave it at the Playa del carmen penger ferry, but also rent a car in cozumel (to explore the island too) this way we could take the only 45 minute penger ferry and then use our parked car to go to the ruins, etc??