Originally Posted by
MSPeconomist
However, I think you're being a bit optimistic about what can realistically be done on travel days. Even with just three hours between cities, one needs to allow for packing an checking out of the hotel, getting to the train/airport on time (allowing for delays and other problems, including finding the correct track or gate), checking in to new hotel and getting one's orientation, finding local transportation, etc.
I did it recently. The train stations are centrally located in both cities. It took less than five hours door to door from one hotel to the next; actually, closer to four. If the OP catches the 8:00 am train from Barcelona, he'll be in the hotel in Madrid before noon.