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Making use of the observable response time data now available due to computerized testing offers exciting opportunities for the theory and practice of educational measurement. This study extends item response theory by developing a model that incorporates response time data into an IRT inspired model. A joint distribution is used to simultaneously model response accuracy and response time. The conditional distribution incorporates response time into a one parameter logistic model. The marginal distribution of response time uses a two-parameter Weibull distribution. Three simulation studies are conducted to evaluate the accuracy of the estimation techniques. Item difficulty parameters are estimated using marginal maximum likelihood (MML). Maximum a posteriori (MAP) estimation is used to estimate the latent ability and latent person speed parameters. The simulation studies illustrate that the estimation procedures recovered the item and person parameters quite well.