Great question! Would this be in the absence of any other ways of keeping themselves healthy – like water or eating? Let’s say not, because otherwise the person would die of other causes first.
Any form of extreme exercise causes muscle damage – and it is the resting periods between, say, weight-lifting which allows the muscles to regrow and become ‘stronger’ and bigger. So, if you were walking constantly, you would eventually begin to do serious damage to the muscles and ligaments in your legs, because there would be no rest period in which those tissues could heal themselves. I can’t imagine someone lasting more than a few days of constant damage to their legs before they collapsed.
Having said that, I am perhaps biased because I read the short story “The Long Walk” by Stephen King, which describes a game show which involved people walking to death. Have a read, because it is one of his best!
It would depend on how hot it was, how much water and food they had and if they could rest. There was a guy called George Meegan who walked for over six and a half years, covering almost 20,000 miles. He did stop to eat and rest though.
That sounds like an idea for a scientific study to me. You could get a group of people and start them walking until they collapsed and then take an average of how long it took. You’d need to decide lots of things before you started like whether they got food and water and whether they were allowed to sleep.
I think you might have some trouble recruiting people to be in your study though – doesn’t sound like a very nice experience!