Hint!

Try to visualise the train timetable, with just two departures each hour. Sketching a timeline can really help.

What would be the consequences of changing the number of minutes past the hour for each train?

Solution

The train bound for one town leaves just a few minutes after the one bound for the other town.

This means that there is only a very short window of time in which the man could get the second train of the hour, because he always takes the first one that leaves.

For example: train A leaves at 10 past the hour. Train B leaves at 12 past the hour. The man will only catch train B if he arrives just after 10 past but before 12 past.