If I had to guess at the time it's about 15 minutes from MK to Epcot and slightly shorter on the reverse trip. It's shorter going back to MK becausee you don't loop through Epcot.
Just to clarify....the monorail does not go directly from the Magic Kingdom to Epcot. You must transfer at the TTC for the Epcot monorail. The time varies since you might have to wait for both monorails, or you might get them right away.
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