Understanding students' learning characteristics is central to successfully designing student-centered learning. Particularly in the problem-solving area, it is vital to know that students can possess their styles to solve problems, which should be considered central to addressing adaptive learning. To date, analyzing students' learning characteristics has been mainly based on their final answers. However, there is a limit to understanding the thinking process of students with the correct answer, because their responses are, de facto, singular and identical. With this background, we propose an approach for investigating students' cognitive behavior in problem-solving using response time in the process data. In this paper, we analyzed an item in Programme for International Student Assessment 2012 Creative Problem Solving (CP038q1). We analyzed log data from the PISA CPS item Ticket encompassing 30,453 students (7,196 students with the correct answer and 23,257 students with incorrect answers) from 42 countries. We found that students with the correct answer are categorized into four clusters, and the problem-solving patterns of each cluster are distinguishable. We also showed the internal validity of this approach by confirming that students with incorrect answers can also be similarly classified. Our results indicate that allotted response time in an item can shed light on several distinguished problem-solving patterns, which implies that adaptive learning and feedback are vital for them.