Brain teaser "clock observation"

Hey everyone, here is a longer solution that the preblounge team sent me. Maybe it helps you too.

The hour hand of a clock is exactly on the minute mark five times each hour i.e. on the hour, twelve minutes past the hour, twenty four minutes past the hour, thirty six minutes past the hour and forty eight minutes past the hour. Now we will use an equation with two unknowns to solve the problem. Let us suppose that X are the number of hours and Y are the number of minutes past the hour. When the hour hand is on the minute mark, the position of the hour hand is: 5X + Y/12 The position of the minute hand is: Y Thus, when the first observation is made the corresponding equation is: Y = 5X + Y/12 + 6 This is also equivalent to 60X = 11Y - 72. But from what we know, Y can only be equal to 0, 12, 24, 36 or 48. Thus, the only value possible for X and Y are 1 and 12 respectively. This means that the time is 1:12 when the second observation is made. When the second observation is made the corresponding equation is: Y = 5X + Y/12 + 7 This is also equivalent to 60X = 11Y - 84. The possible values for X and Y here are 3 and 24 respectively. This means that the time is 3:24 when the second observation is made. Now we know the time of the first oberservation and of the second observation and can easily calculate the time that has elapsed between the two of them: From 1:12 till 3:24 it is 2 hours and 12 minutes.

Hi,

It would be helpful if you provide more details.

If that is the case:

"The hour hand is exactly at a minute mark, and the minute hand is six minutes ahead of it in the first glance. When the clock is looked at again, the hour hand is exactly on a different minute mark, and the minute hand is seven minutes ahead of it this time."

Then the solution is:

In the first observation, the time was 1:12. In the second observation, the time was 3:24.
Therefore, 2 hours and 12 minutes have elapsed.

Best