I've decided to put the new seed feature to work to illustrate how deceiving distances are in the game!
The Minecraft Marathon Challenge1 Start a world with the seed "Marathon"
2 Make your way 40.195 km (~26 miles) east
(any x, z < -41,810.5)3 If you win then brag about your time, difficulty, cheats and mods.
HintsYou start out facing east so don't just stand there looking around. RUN!!!
F3 toggles debug info with your Minecraft coords on screen along with other info.
Spawn point is x: -121.5, z: 384.5.Wikipedia says a marathon is 40.195 km or 26 miles and 385 yards.
Boats might speed you up if you collect, build, place and start them fast enough. They can also take you to a remote spot at night so you can spend whatever time you will be crafting or smelting without the need to build shelter or just run through the night.
I also suspect mushroom soup is the best way to heal fall and mob damage. Make some bowls early on and keep an eye out for them, especially at night.
I think I saw the third sunrise around the time I had made it 4 km (normal difficulty, no cheats or mods) so total times of around 20 Minecraft days (6.67 hrs) should probably be expected. I was running/boating both day and night so double that if you won't be running straight through the night.
One runner's defense against skeletons is to try to kite other monsters between you and the skeleton so it hits them and they turn on the skeleton.
The runner's best weapon is probably flint and steel used to set tiles behind you on fire but only if you don't break it by spamming it all the time. Wait for your enemies to burn out before you catch them on fire again. Keep an eye out for surface iron and smelt a bar early.
If you are thinking about making armor, you should work out that the most cost effective armor pieces are: (from memory; best to worst) chest, legs, feet, head.
EDIT: Changed because Aklyon pointed out spawn points change even with the same seed.