Karen can read 10 pages and complete 15 math problems in 30 minutes. How long will it take her to do her homework if she has 30 pages to read and 45 math problems to complete.
Karen can read 10 pages and complete 15 math problems in 30 minutes.
So, Karen can read 30/10 = <<30/10=3>>3 sets of 10 pages in 30 minutes and she can complete 45/15 = <<45/15=3>>3 sets of 15 math problems in 30 minutes.
This means Karen will spend 30/3 = <<30/3=10>>10 minutes to read 30 pages.
She will also use 30/3 = <<30/3=10>>10 minutes to finish 45 math problems.
Therefore, Karen will spend a total of 10 + 10 = <<10+10=20>>20 minutes to do her homework. Answer: \boxed{20}.