Question 1007804
Well, this one involves an infinite series that is to be added...
When the minute hand travels 60 minutes, the hour hand travels 5 minutes.
When the minute hand travels 5 minutes, the hour hand travels (1/12)(5) minutes.
When the minute hand travels (1/12)(5) minutes, the hour hand travels (1/144)(5) minutes.
When the minute hand travels (1/144)(5) minutes, the hour hand travels (1/1728)(5) minutes...and so on...

Thus we can add up the travels of the hour hand as an infinite series,
{{{S = a1 / (1 - r)}}}
where a1 = 5 and r = 1/12 and we get
S = 5 / (1 - 1/12) = 5 / (11/12) = 60/11 minutes or 5 5/11 minutes past 1 o'clock.