Gatsu (from the manga Berserk) won't bat an eye to face this task, but i fear that would be difficult to accept Gatsu as the "average guy". :)
As already stated the average guy with a heavy plate armor won't even walk for a tenth of the supposed distance, especially with such a zombie density.
Maybe can be interesting to see, modifying some OP requirements, what a "lone knight" could do in a similar situation.
1: the walking distance.
50km is way too much for a sedentary person, but not impossible for a quite trained one. I'm not talking of professional athlete, there are a lot of amateur athlete that do marathons (42+ Km), therefore a young guy, who was military trained for one year, has a chance to close the distance.
Actually, 50km is exactly the lenght of the "Kepi" march, part of the French Foreign Legion training, in which the legionnaire have to march in "full combat gear carying rifle, helmet and 30 kg load".
Without the huge amount of zombies (and imaging that a plate armor is comfortable enough) the distance is an acceptable requirements.
2: the armor and the weapons.
A full plate armor is more of a hindrance than a help. It cause additional unnecessary wheight, is feasible but for sure uncomfortable to run wearing it, it makes a lot of noise (and probalbly it shines, not helping to avoid zombies) and the standard helmet reduces the field of view.
I would go with a leather suite, covered with grease (you really don't want to give grasp points to the zombies, or the 40+ Kg armor will easily rise to 200+ Kg and you'll be stucked). An hockey or football helmet, with some protection for the neck, will complete my defence against biting and scratching.
The weapons should be 2 because you are supposed to face a huge number of zombies, and two arms to wear out are better than one. Since you are supposed to move constantly you only have to cripple the zombies that are on your path. You don't have to slash anything that's particullary strong, therefore something that's lightwight and handleable would work well, i'd go with a couple of tomahawks or the traditional machetes.
3: the zombies [measue unit: Z] density.
You stated that the guy should expect 2.5 KZ/Km -> 2.5 Z/m.
You didn't say how wide the road would be, therefore we/i assume 10m for simplicity -> 0.25 Z/m^2.
Assuming that the guy needs only 1m wide track to proceed, he will face 12.5 KZ. For sure the Zs tend to mass against the guy, therefore the density won't be uniform and we should at least double the previous number -> a total of 25 KZ on the path.
25K machete hits to clear the path can't be sustained from anyone but, if we reduce the number by one order of magnitude, maybe is not impossible.
2.5K is still a lot of hits, and you also have to walk 50km: the only possibility for the guy is to have some triathlon ironman-level physical training.
In this case it could be feasible:
- walking 50km is affordable for an ironman athlete, he's supposed to RUN for 42+ Km.
- he won't swim, but he needs to hit some skulls with tomahawks. The arm movement is quite similar to front crawl style. The ironman athlete is supposed to swim for 3860m, and a good athlete will complete one 25m pool with 15 arm swings. This means that the ironman is supposed to do 2316 arm swing, with a little more effort he could swing the arm another 186 times and actually clear his path.
- an ironman athlete should also ride a bike for 180Km, we can dedicate this "energy reserve" to deal with the armor additional drag and to manage critical events (particularly annoying Z groups, sprints to gain time to drink).
4: food and water.
The food isn't as important as water, you have to eat for sure but 1 Kg of high energy density food will be surely enough to finish the trip, the water is a problem.
During a race, an ironman athlete needs 1.1 liter/h, the fastest athlete can finish the race in a little more than 8h but since our guy must deal with a lot of distractions he should plan a 16h run. Moreover, he won't use a triathlon suite but a (hopefully) light armor instead! Sweat increase, therefore 17 liters of water are definitely required, and this means that he needs to carry at least 18Kg + other gears. The plate armor is really a no-go option because of the weight.
- an average guy, with a metal plate armor, facing 125 KZ on a 50 Km path -> he doesn't stand a chance.
- an ironman athlete, with a leather armor, facing only 12.5 KZ on a 50 Km path -> if lucky, he can hope to reach a safe place after 16 hours of fight, outworn but alive.
For the records: for few people this trip wouldn't be anything special.
For instance, we can consider James Lawrence, a man who completed 50 ironman-length triathlons in 50 consecutive days.
Apparently, provided he could rest every night, this guy could kill at least 6.25 BILLIONS of zombies on a streak! 0_0
He's not an athlete, he's a war machine...