Dear 100 Hour Board,
How far is it humanly possible to walk in a straight line, assuming you couldn't bring anything with you, you were well fed and watered at the beginning, and you were allowed to stop and rest at will? How would that change if you could bring as much supplies as you could carry? Or if you had a bike? What if there were no restrictions, and you had all the world's scientific knowledge at your disposal, but you could still only bring what materials you start with at the beginning of the infinitely long theoretical road?
Not very far, because the Earth is round, so a straight line would go out into space.
-->Captain Obvious Literal
At first, I thought the emphasis was on how hard it was to walk in a straight line (e.g., it's really easy to wander around in circles, especially in rough terrain), but I'm pretty sure you're asking how far someone could walk without extra supplies before they die. On that assumption, I'll throw out some guesses for each of your scenarios. Some basic assumptions: we're on level ground, it's cool enough outside that you don't sweat easily, and it's cloudy so you aren't getting baked by the sun.
In the first scenario, water will definitely be your limiting factor, unless we're assuming the person has access to a stream or something. A moderate walking pace is about 3 miles per hour; let's assume that our person is in pretty good shape and could walk, say, 10 hours a day. The usual rule of thumb is that you can go about three days without water, although it'll depend on how hot it is, how hard you're exerting yourself, etc. By the second day, I'll say you're only at 60%, and by the third, you're at 20%. I think it's pretty safe to say you'll walk less than 3*10*3 = 90 miles, and probably more like 3*10*1.8 = 54 miles. (Even if you're still alive after the third day, you won't be going anywhere fast.)
What if you had a bike, with attached bike trailer, and all the water/food you could carry in the trailer? A typical bike trailer can carry around 100 pounds; let's call it 50 kg. That's 50 liters of water. An adult male age 19–30 needs around 3.7 liters of water per day. You'll obviously need more since you're pedaling a bike, but let's say you take it easy (remember, you're also hauling a trailer) and go 12 miles per hour. I'll guess you'll double your water needs, so call it 7 liters per day, meaning you run out after 7 days (but you have another three days, as above). Let's assume you're in wold-class, Tour de France shape, and still assume 10 hours per day, in which case you'll travel around 12*10*(7 + 1.8) = 1056 miles. This is very unrealistic, in my opinion, but it's an upper bound, anyway. (What about food? I'm assuming you have something really calorie dense, like sugar and vegetable oil, so you can add another few kilos on your bike trailer and not make a difference.)
No restrictions: does a spaceship count? We've repeatedly put men on the moon, which is 240,000 miles away, so we could clearly go at least twice that far with just what we started with and without running out of air, food, etc. We're also discussing manned missions to Mars; they won't happen soon, but could happen in the next couple of decades. I found calculations for a Hohmann transfer orbit from Earth to Mars, which is one of the proposed trajectories for a manned Mars mission; in the particular scenario outlined in the calculations above, on the way to Mars, a craft would cover 1.4 billion km (890 million miles), and I'll assume the same on the way back. Unlike my calculations above, I feel like this is a lower bound, not an upper bound; I think we'll just keep getting better and better at keeping people alive over long distances. Who knows what we'll be able to do in 100 years?