To recognize vowels in speech, people use acoustic information such as the spectral quality and duration of the vowel. Typically, the contribution of these cues (i.e., cue weighting) is inferred from categorization data. Researchers have learned that the two cues are processed differently making it difficult to interpret the categorization data alone. Although eye tracking is a promising method in speech perception, it requires an explicit linking hypothesis and is based on aggregated data. We advocate the use of quantitative cognitive modeling of reaction time data instead. In our study, we analyze data from an experiment in which listeners categorize the Dutch /A/ and /a:/ vowels. Using the linear ballistic accumulator model, we found that that the differences in the spectral quality and duration contributions were driven by how the cues affect speed of information processing. The influence that spectral cues have on speed of processing was not only larger than duration, but larger for /A/ than for /a:/. We found that listeners were biased to respond /a:/ and this was driven by them processing /a:/ vowels faster than the /A/ vowels. The duration cue was processed faster for the /a:/ vowel compared to the /A/ vowel. Finally, we found that participants did not wait until the vowel offsets to begin processing duration information.