EDIT::: FASTER WAY:::
What you do is you start out at full speed, go full speed until you get to the barrel and all your Ram Fatigue goes away, from there you can go at full speed slowing down to a canter occasionally. If you time it right, you can go at gallop speed most of the time for only canter speed fatigue. When getting the barrel you only need to go to the dwarf that is before the actual barrel thrower. You do not need to go to the apples behind, using this method it only slows you down, this method is faster anyways. When you are throwing the barrel for the tickets do a jump turn so that you land about even to the Brewfest flag, this should throw it and you are already headed back to the apples, remember to go full speed at that time.
Overview:
* Turn as you jump, preferably using the mouse.
* Between the barrel and the start, you can travel at full speed. Do so.
* Between the barrel and the keg giver, you need to drop to a canter now and then. If you drop to a canter then immediately switch back to a gallop, you can pretty much travel at gallop speed for canter fatigue.
* It's faster to watch your fatigue and skip the barrel in the back.
::: EDIT OVER :::
I will keep this here because it is easier for people whose computers have to much lag to do the method posted above or cant time it right .
When doing the fetching for the brew, you can run at GALLOP speed the whole time! All you have to do is make sure that you run by the first barrel of apples on the way to Kharanos, then when you get to the guy who throws out the barrels, DON'T TURN AROUND YET, go another 15 yards or so and there is another barrel!! You can then run past this barrel, still at gallop speed, and make it to the next barrel before your ram gets exhausted. You can also make it back to the guy whom you throw the beer to for the tickets. This has easily added 9+ more tickets at the very least to my ticket total. Hope you enjoy it!