In a 90-minute time period, Gina watched TV, texted a friend, and read a book. She spent 3/5 of the time watching TV and 1/6 of the remainder of the time texting a friend. How much time did Gina spend reading?

Gina spent 90 x 3/5 = <<90*3/5=54>>54 minutes watching TV.

So, 90 - 54 = <<90-54=36>>36 minutes was the remainder of the time.
Then, 36 x 1/6 = <<36*1/6=6>>6 minutes was spent texting a friend.
Thus, Gina spent 36 - 6 = <<36-6=30>>30 minutes reading. Answer: \boxed{30}.