Back to the books, TCF?
BOAC I hope that I'm not having a 'senior moment'!
If, for example, that the aircraft is at 20000 feet and the cabin is at, say, 2000 feet, and, that the aircraft is descending at 2000 fpm it will take ten-minutes for the aircraft to reach zero feet (assuming a sea-level runway and 1013). If the cabin RoD is set at 200 fpm both aircraft and aeroplane will arrive at sea-level at the same time i.e. zero diff pressure; just what the good doctor ordered.
If you now increase the aircraft RoD to, say, 4000 fpm, the aircraft will now take only five-minutes to reach sea-level; however, the cabin is still descending at 200 fpm and, during that five-minute period, will have descended by only 1000 feet i.e. the cabin alt will be 1000 feet... or at least that's where it wants to be; however, zero diff pressure would have been achieved much earlier than the landing.
Please correct me if I'm wrong!