most of sth, especially a period of time; more than half of sth :
The journey took her the better part of an hour.
most of sth, especially a period of time; more than half of sth :
The journey took her the better part of an hour.
Oxford Advanced Learner's English Dictionary. Оксфордский английский словарь для изучающик язык на продвинутом уровне. 2005