Caroline can sketch 6 cartoon strips in ten hours. How long will it take her to sketch 9 strips?

Caroline can sketch 6 cartoon strips in 10 hours, so she can sketch 6/10 = <<6/10=0.6>>0.6 cartoon strips in an hour.

Therefore, it will take her 9/0.6 = <<9/0.6=15>>15 hours to sketch 9 strips. Answer: \boxed{15}.