Is the man with the cart going on a road, or cross-country? Do we count the caloric cost of building/maintaining the road in this equation? Is it a dirt road, a paved road, cobblestones..?
Expeditions can set up supply depots along the route, to be used for the final push, so it's not quite a fair comparison.
If you can carry enough food for X days, you could travel out X/4 days, leave a cache with enough supplies for X/2 days, then travel back with the last X/4 days of supplies. During the actual push, take X/4 from the cache on your way out, and X/4 from the cache on your way back. By using the cache, your range has increased from 0.5X to 0.75X. (This is a simplified example that assumes only a single cache of supplies is being used, and that the same size party is used for both trips.)
More extreme resource planning can also be used for expeditions, though can raise questions of ethics. The first successful expedition to the South Pole [0] set off with 52 sled-dogs, 45 of which survived the first month of the expedition. At that point, the supplies were light enough that they only required 18 dogs for the final push. The remainder were killed and butchered, both to reduce the number of mouths to feed and to provide food for the humans and remaining dogs.
It was a real morale hit to the men as they had grown to really like the dogs. I guess the lesson is to never to make friends with something you are going to have to eat. Though the effectiveness is indisputable given Scott's failure.
On the use of dogs as an expendable resource, Scott said "One cannot calmly contemplate the murder of animals which possess such intelligence and individuality, which have frequently such endearing qualities, and which very possibly one has learnt to regard as friends and companions.", poor guy. Quite the gentleman.
Well, he was of his time of course. It's not realistic to expect him to have an anachronistically enlightened view of animal rights (beyond what might be considered common even today). It wasn't anything he wasn't prepared to do himself for that matter. I think his general standard of interpersonal behaviour more than allows him the descriptor of gentleman - by the standards of his day, naturally.
(As an aside, he did pioneer the use of motor sleds for antarctic expeditions, but that was a disaster for him too.)
>in practice about a month and a half’s logistics buffer is the maximum that’s possible and even doing that is expensive.