Problem solving is a critical feature of highly quantitative physical science topics, such as chemical kinetics. In order to solve a problem, students must cue into relevant features, ignore irrelevant features, and choose among potential problem-solving approaches. However, what is considered appropriate or productive for problem solving is highly context-dependent. This study is part of a larger project centered on students' integration of chemistry and mathematics knowledge and skills. The data for this study came from semi-structured interviews with 40 general chemistry students using a think-aloud protocol. Interview prompts involved students working through two chemical kinetics problems, one involving a second-order system and one involving a zero-order system. In both cases, students could solve the problem using the data provided and relevant equations, or by taking a conceptual approach and considering the relationship between quantities. Using the resource-based model of cognition as our theoretical framework, analysis focused on characterizing the productive and unproductive problem-solving routes used by students. Findings emphasize the role of using conceptual reasoning and reflecting on one's work during problem solving, which have implications for instructors as they guide students to think about chemical kinetics and to solve problems across quantitative topics in science, technology, engineering, and mathematics.