There are 7 days in one week so one week and 2 days = 7+2 = <<7+2=9>>9 days
Call the time Ethan spends learning tricks e. Alexa spent 9 days on vacation which is 3/4ths of the time Ethan spent learning 12 fencing tricks, hence (3/4)e = 9 days
If we multiply both sides of this equation by 4/3, we get e = (4/3)*9 days = <<(4/3)*9=12>>12 days
Joey spent half of 12 days which is 12/2 = <<12/2=6>>6 days to learn swimming
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