The question I pose to you is, for a hike like this, or any other for that matter, how do you determine when you should take a rest break? Over the years I have used a number of different means to help try and answer that question. When I first started hiking I took a break when I got tired. In 1970 I learned from Paul Petzoldt that taking a break when you are tired doesn't make sense. You're much better off taking a break BEFORE you get tired. When I got more experience hiking I used time as an indicator of when I might take a break. Early on I would generally hike an hour and rest ten minutes. I quickly learned that when leading groups and carrying heavy packs that was too long a time span to go without a break. I found that hiking twenty minutes with short breaks seemed to work better. I found it was extremely helpful to have pre-determined break times. It allowed people who were not as strong, in as good physical condition, or mentally tough to have something to look forward to. They learned that if they can just make it the next twenty minutes or maybe even the next five minutes that they would get a break. It seemed to work pretty well.
Flash forward to this April when, for my birthday, I hiked up Ampersand Mountain with my great nephew and niece aged 10 and 9. Now I have a GPS with a built in altimeter. How did we determine when to take breaks? I told them we'll take a break when we travel 1.5 miles or gain 400 feet in elevation whichever comes first. We didn't take a break on the approach until we hiked 1 and a half miles. Then we started taking much more frequent breaks as we gained elevation quickly. It worked great... Well at least the rest breaks worked great. Late season ice prevented us from summiting but that's a story for another time.
BOTTOME LINE: Take breaks BEFORE you get tired. You want to have a reserve of energy in case you run into an emergency situation. Use time, distance, and elevation gain to help determine when to take a break.