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At the moment, I'm reading The Hobbit, and I just watched the first movie, The Hobbit: An Unexpected Journey.
It was fun to note where the movie was following word by word the book, and when it gave itself more freedom.

However, there's one point that baffles me a bit: the encounter with Radagast.
Radagast seems to live within Mirkwood, notices quite a number of strange dark things in the forest, and visits Dol Guldur, where he meets the shadow of the Necromancer. After seizing the Morgul blade, he escapes swiftly aboard his rabbit-led sled.

At the same time, Thorin's company is still far west of the Misty Mountains, somewhere between Bree and Rivendell. They come across the three trolls there, visit their near-by cave... and that's when Radagast runs into them, on his sled, as if he was still running from the Necromancer's minions!

How is it possible, while Thorin's company is far west of the Misty Mountains, and Radagast is far east, within Mirkwood?

The trip across the Misty Mountains is a long and dangerous one, even for a wizard accompanied by a party of warriors, as we're shown later. I can hardly believe Radagast crossed the mountains in what seems a blink of an eye.

Is there something I missed to explain this course of events?

As the meeting doesn't happen in the book, an out of universe explanation is just that Peter Jackson thought it would make a good scene.

Searching for an in universe explanation of how Radagast could make this journey and how it could seem so short, I can come up with the following points:

• Dol Guldur is at the southern end of Mirkwood. Radagast may have traveled through Rohan round the southern end of the Misty Mountain. That avoids the problem of how his sled could cross the mountains.
  


• If we assume that he is looking for Gandalf and knows of his interest in the Shire, he would probably head north to the great road and then follow it west towards the Shire.


• Traveling on the great road, he could have seen come sign that suggested Gandalf had been on the road and turned off to the north. This may seem unlikely, but Radagast appears to be skilled in woodcraft and it's just possible that Gandalf deliberately left a sign that friendly eyes would recognise.


• Radagast could have followed the trail of Gandalf (and the dwarves) from the road until he met them. This could explain how Radagast found them.
  


• Time can be compressed in movies, so although Radagast's journey appears to take very little time, it could have taken weeks or months. This could explain how the journey seemed so quick.