Working their way through - Idioms by The Free Dictionary
work (one's) way through (redirected from working their way through)
work (one's) way through
To stay engaged in a task continuously. Often used when the task is long-term or plodding. Kate is working her way through college, but it's taken a while, as she's only been able to attend classes part-time. I have to work my way through any book I start, even if I don't like it very much.
work, etc. your way through something read or do something from the beginning to the end of something: He worked his way through the dictionary learning ten new words every day. ♢ He’s eating his way through all the restaurants that are recommended in the Good Food Guide.