An examinee faced with a test item will engage in solution behavior or rapid-guessing behavior. These qualitatively different test-taking behaviors bias parameter estimates for item response models that do not control for such behavior. A mixture Rasch model with item response time components was proposed and evaluated through application to real test data and a simulation study. The analysis of extant data indicated that a two-class solution fit better than a one-class solution and that 15% of examinees engaged in rapid-guessing behavior. Moreover, solution behavior examinees had substantially higher average ability scores than rapid-guessing examinees. Results of the simulation study indicated that the parameters were recovered well.