I haven't done any long distance walks, but I've done ultra-distance bike rides (600 miles/ 2 days), and swims (20+ mile events)
Running is my weak spot, (I hate it), but I've found that universally across all distance events, there comes a point you become mentally fatigued. Yes, you're sore and tired, but around hour 8 (between 24 and 32 miles), you'll just be thinking to yourself "what the hell am I doing? This sucks."
For me, I find mind games help. Count every mile as it's own % to finish. First mile in? Easy. 2%. Next mile? 2%. They add up quick. And when you're 65-80% through, you think back to how easy each 2% is... And keep pushing.
Have someone to talk to / walk with! Nothing takes your mind off what your doing better than some friendly company.
Lastly, nutrition/hydration. I won't really get into this. Not enough time or space in a forum post. ;-) You start really attention to what you put into your body a week out. Recognize that on the day of the event, especially towards the end, your body is going to start shutting down unneeded functions in order to conserve and channel energy to moving. One of the first things to shut down is your metabolism. You stop processing new nutrients. Because of this, staying on top of your hydration, salts, and sugars early is very very important.
I'm not sure what time frame they allow for you to finish, but most likely, if you need to stop and rest, stop. You'll have the time. If they give you a full 24 hours, all you need to average is 2 MPH.
And finally, training. Generally, 13 Miles is good. You'll want to slip one our two longer distance in (24 to 30), but probably nothing more. Training between 25% to 50% of the event distance is going to allow your body to train for the "feel"of the longer distance, without stressing too much.
Cheers!
Oh, and I forgot to finish my earlier thought. After you get past the "What the hell am I doing?" and you reach the end... Best feeling in the world. Even if standing up is hard to do at that point. ;-)