Starting from an explicit scoring rule for time limit tasks incorporating both response time and accuracy, and a definite trade-off between speed and accuracy, a response model is derived. Since the scoring rule is interpreted as a sufficient statistic, the model belongs to the exponential family. The various marginal and conditional distributions for response accuracy and response time are derived, and it is shown how the model parameters can be estimated. The model for response accuracy is found to be the two-parameter logistic model. It is found that the time limit determines the item discrimination, and this effect is illustrated with the Amsterdam Chess Test II. (Contains 1 table, 9 figures, and 4 footnotes.)