Mdthbs

I booked a flight for me and a friend that goes from Tel Aviv to Barcelona. It connects at Athens International (ATH) and leaves us an only an hour for the connection. That is, the flight arrives to ATH exactly one hour before the next (connection) flight departs from ATH. The first leg is Aegean 925 and the second leg is Aegean 712 (so Extra Schengen > Intra Schengen in the Aegean connection terminology)

The problem is, my friend has an injury that prevents her from walking fast, so I want to make sure that an hour would be long enough for the connection assuming normal walking speed.

I talked with both the airline and the airport and the only thing they would say is that the arrival and departure will both take place from the same terminal, and that 55 minutes should be enough. But we have no idea how big the terminal is, and specifically how long it would take from a worst-case scenario arrival gate to departure gate assuming normal (female) walking speed.

Be prepared to miss your connection. The airline will take care of you meaning meals and accommodation as necessary and required to rebook you on their next flight to Barcelona (if there are available seats). While they are not required to, they also might use another airline to get you to Barcelona quicker. They are more likely to do this with an airline they are in alliance with and Aegean is part of the Star Alliance which is very strong in Europe -- they might be able to route you through either Frankfurt or Munich (with Lufthansa) or Zurich with Swiss. Make no demands, be polite and they will likely be more willing to help. Be prepared to overnight in Athens (if you had checked luggage you will get it): your flight is scheduled to leave very late in the evening and it's not likely you will have a flight during the night.

Now, back to the original question about the airport. The problem is not walking, ATH is a surprisingly compact airport compared to most primary capitol international airports, walking the main terminal across, I dunno, takes at most 20 minutes if that. There's a satellite terminal which takes a bit of a walk but AFAIK Aegean doesn't fly from there, I checked and today they were flying to Barcelona from the B gates (the satellite gates are A30-A39).

No, your problem is the border. There is just not enough staff now they implemented stricter controls as per EU Regulation 2017/458 (Athens asked for and got a long time to implement it but as of 2019 April they now do it). Your connection was already tight: it is calculated from the minute when your plane lands -- but you need to deplane (10 minutes at least but if they are using a bus it can be more), walk to border control, get through border control and get to the departure gate before it closes (so you can easily dock another 15 minutes here).

Also Ben Gurion is not known for being punctual, these days, they closed Sde Dov and the airport is still struggling with the added traffic. So you can reasonably expect your incoming flight to be late and with that sort of already tight connection, even a few minutes are a problem. Or it's an advantage, depending on how you look: if your incoming flight is late then EU Regulation 261/2004 kicks in as you very likely you will be delayed by over three hours and then you are also entitled to 400 EUR compensation. See this answer for more.

Finally, you might just get lucky and your outgoing flight might be late as well, when I am typing this on Aug 25, 2019 it certainly was, by 51 minutes.