12.4.4 Various Olympiad problems

Problem: John, leaving the house, looked at his watch and saw that the line, dividing the angle between the hour and minute hands in half, passes through number 12. When he came to school, the line, dividing the angle between the hour and minute hands in half, passed through the mark, corresponding to 13 minutes. How long did John walk from home to school if it is known that he left after 8:00, and arrived at school before 9:00?