Alexa was on vacation for 3/4ths of the time it took Ethan to learn 12 fencing tricks. Joey spent half as much this time (that Ethan spent learning the tricks) learning to swim. If Alexa spent a week and 2 days on vacation, how many days did it take Joey to learn swimming?
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
#### 6