Carmen went rock climbing at the climbing gym for 1
1
2
hours on Thursday. On Saturday, she went to Castle Rock State Park and climbed for 1
1
2
times as long. How much time did she spend rock climbing in all?
On Thursday, Carmen spent 1 + 1/2 = <<1+1/2=1.5>>1.5 hours rock climbing.
On Saturday, she spent 1.5 * 1.5 = <<1.5*1.5=2.25>>2.25 hours rock climbing.
Therefore, Carmen spent a total of 1.5 + 2.25 = <<1.5+2.25=3.75>>3.75 hours rock climbing. Answer: \boxed{3.75}.
To find out the total time Carmen spent rock climbing, we need to add the time she spent at the climbing gym on Thursday and the time she spent at Castle Rock State Park on Saturday.
Carmen spent 1 1/2 hours at the climbing gym on Thursday.
Carmen spent 1 1/2 * 1 1/2 = 2 1/4 hours at Castle Rock State Park on Saturday.
To find the total time, we add the two values: 1 1/2 + 2 1/4 = 3 3/4 hours.
So, Carmen spent a total of 3 3/4 hours rock climbing.