Hello. We will be arriving Barcelona at noon on a Saturday and would like to connect to Madrid on a 2:30pm flight. Is that enough time to clear custom and get on the 2:30pm Madrid flight? We do not need to wait for baggage. Arrival flight and departure flight should be in the same terminal. How long does it take to get through custom? How far are the furthest gates in terminal T1? Thanks.
Are they all on one ticket? You will have to go through Schengen Immigration in Barcelona. Generally, if an airline sold you a ticket, its a legal connection, and they think you can make it. If your inbound flight is delayed, causing you to miss the connection, there should be a later flight you can get. Check the schedule for that airline.
Off hand, 2 1/2 hours seems plenty.
Customs (aduanas) is a 2 second delay.
I always suggest that one first look at the options for changing their ticket to fly directly to their desired destination. It would be very worth paying a reasonable premium for the easy and comfort.