<p>Careless respondents inject noise into data which can distort research findings and compromise model fit. To address this, factor mixture modeling (FMM) has been widely used to identify careless respondents. Traditionally, researchers have relied on reverse-worded questions in FMM to facilitate the detection of careless responding. With the rise of online data collection platforms, response time has appeal as a means for understanding careless behavior. We introduce a Bayesian FMM that leverages this rich source of information to identify careless respondents. By jointly modeling responses and response time, this approach effectively identifies careless individuals rushing through the questionnaire without providing responses that reflect the to-be-measured traits. Our simulation studies demonstrate that this model accurately estimates parameters and classifies respondents as either attentive or careless, while maintaining error rates within acceptable limits. Furthermore, integrating response time enhances model convergence and the precision of classification and estimation. Using mediation models as an example, we illustrate how social science researchers can use this FMM approach to address careless responding in substantive research. An empirical study further tests the applicability of the proposed model in real-world scenarios, comparing its conclusions with traditional methods. To support its use, we provide an R function to streamline implementation.</p>