UniChris

I'm not in good shape, I'm not that much short of twice your age, and this past weekend I rode a century... on only half a bike.

As others have said, this is more of a tolerance challenge than an athletic one. You'll need to do work, but mostly your body will need to tolerate the stress of the saddle, riding position, repetitive motion, heat/sun, etc. The faster you go the more energy you'll expend pushing against wind drag, the slower you go, the more toll those incidental stresses will take, but there's a speed that will work for you, and you'll soon find it.

You can probably do 15 miles just by deciding to. 26 to make a bike "marathon" within a week of that. Step it up to 50K (31 miles), 40, 50, at that point you could probably do the event on confident determination, but if you get in one last training ride of a Metric Century (100 km or 62 miles) you'll be certain that it's going to work, outside of any equipment failure or injury that support is specifically there for.

Find somewhere interesting to go, get on whatever sort of bike is available and go as far as you can, at whatever pace feels comfortable. When the seat hurts, stand up on the pedals and coast for a minute, when that doesn't work, stop and get off the bike for five minutes. If you're on a route you know, try to hold out a little longer until you make it to that next road crossing or parking lot or gas station or whatever. Do this regularly from now until then, a little further each time between now and the event. Be smart about hydration, electrolytes (especially sources of sodium and potassium salts), food, and sun exposure. Get bike shorts that fit and chamois cream. Run Strava on your phone, not to compete with others but to see how you are doing vs the previous ride. Not immediately but eventually, get a cheapy bike computer like the Bell 150 and work on holding a steady pace reasonable to flat or uphill conditions.

Review relevant threads here to find "energy food" and drink mixes that you like, try them, and make sure you react well; be wary of accepting unfamiliar freebies on ride day, as not everyone reacts well to all "engineered food". Make sure some of your training rides start as early in the morning as you'll need to be heading to the event ride, so you are used to what it's like to get out the door, and to sleep before that, or to ride on none (been there, done that) Think about ride day "bathroom strategy" and figure out what works for you.

I'm not immediately seeing how much time you have to complete the ride, but I'm going to guess it will be enough for just about any reasonable effort on just about anything with two wheels but a fat bike. If it's really looking like it's not going to work for you (and that seems unlikely) they mention the option of switching to a shorter route. Likely you'll find that net distance-per-hour pace (inclusive of rest stops) you can sustain on your 26, 31, etc training miles continues right through to 78, though expect to bog down some in peak afternoon sun compared to early morning or dusk hours.