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?

In 90 minutes, Gina spent 90 * 3/5 = <<90*3/5=54>>54 minutes watching TV

The remainder of the time she had was 90 - 54 = <<90-54=36>>36 minutes
She spent 36 * 1/6 = <<36*1/6=6>>6 minutes texting a friend.
Thus, Gina spent a total of 54 + 6 = <<54+6=60>>60 minutes watching TV and texting.
Therefore, Gina spent 90 - 60 = <<90-60=30>>30 minutes reading. Answer: \boxed{30}.