Public transport administrators rely on efficient algorithms for various problems that arise in public transport networks. In particular, our study focused on designing linear-time algorithms for two fundamental path problems: the earliest arrival time (\textsc{eat}) and the fastest path duration (\textsc{fpd}) on public transportation data. We conduct a comparative analysis with state-of-the-art algorithms. The results are quite promising, indicating substantial efficiency improvements. Specifically, the fastest path problem shows a remarkable 34-fold speedup, while the earliest arrival time problem exhibits an even more impressive 183-fold speedup. These findings highlight the effectiveness of our algorithms to solve \textsc{eat} and \textsc{fpd} problems in public transport, and eventually help public administrators to enrich the urban transport experience.