In recent years, advanced driving support systems have been introduced in automobiles. When using such systems, drivers have to engage in two parallel tasks: driving a car and operating the systems. However, elderly people have some difficulties in engaging in such a dual-task. Based on the model-based approach using a computational cognitive model, this paper examines the relationship between the difficulties and the decline of two cognitive abilities in elderly people: time perception and working memory capacity. Results of the simulations showed that each decline caused a different type of problem independently. Specifically, the decline in the abilities of time perception led to poorer driving performance, and the lowering of working memory capacity caused failures of the button press operations.