Yes, it would take a while.
First of all, he could only cover about 2 miles in an hour cantering on horseback. The horse couldn't canter all day, which means he'd be able to ride for maybe 8 hours. Thats a maximum of 16 hours a day, with time to hunt, stop and eat, sleep, etc. Plus, being royalty, he'd want to cook the food, his horse would need plenty of rest. That's a lot of time from Minas Tirith to Rivendell.
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"What mortal feels not awe/Nor trembles at our name,
Hearing our fate-appointed power sublime/Fixed by the eternal law.
For old our office, and our fame,"
-Aeschylus, Song of the Furies
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