Artificial intelligence and data mining techniques offer a chance to make education tailored to every student. One of possible contributions of automated techniques is a selection of suitable problems for individual students based on previously collected data. To achieve this goal, we propose a model of problem solving times, which predicts how much time will a particular student need to solve a given problem. Our model is an analogy of the models used in the item response theory, but instead of probability of a correct answer, we model problem solving time. We also introduce a web-based problem solving tutor, which uses the model to make adaptive predictions and recommends problems of suitable difficulty. The system already collected extensive data on human problem solving. Using this dataset we evaluate the model and discuss an insight gained by an analysis of model parameters.