Using what map? I can't find a scale on my 4e maps, but on the 3e maps I've seen the distance from Wroat to Arcanix is a bit under 1000 miles. The city of Passage is a bit further and probably easier to get lost in.
You're right, I used my scale* incorrectly (in my defense, it was late and I was tired). From Sharn to about Fairhaven is roughly 1900 straight-line miles (give or take). I've never seen an actual journey that
was straight line, but that's a different issue.
If you're looking at over-land from Wroat to Fairhaven then it is shorter (about 1800 miles, 1700 as a crow might fly).
Note that Arcanix is a
village. While possible, it is difficult to "get lost" in a village unless the villagers are actively helping you. The (presumably) Brelish exiles would be doing well not to be exposed / lynched by the villagers.
*3.5 ECS; I don't have the 4E one handy.
As
lukelightning said, the journey can take as long as you want and be as eventful as you desire. The time on foot would be roughly 12 weeks, possibly longer depending upon weather and terrain issues. Riding, it depends upon the speed of the mounts (Nightmares are faster than Horses, and Great Wyrms can get some decent overland speeds going). By lightning rail, well, you have to figure the relevant distances along the rail network. Air ship would be the fastest but isn't always the best (so many modules crash airships).
Good luck.