Can you calculate the time that has elapsed between the two observations?

Question

At a certain point of time someone observes a clock and find out that the hour hand is exactly at the minute mark and the minute hand is six minutes ahead it. The clock is observed again to find out that hour hand is exactly on a different minute mark but the minute hand is seven minutes ahead of it this time.

Can you calculate the time that has elapsed between the two observations?

Answer 1

2 hours & 12 minutes

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The hour hand is exactly on a minute mark five times per hour - 0/12/24/36/48 mins
Let X be the number of hours, and Y be the number of minutes past the hour. When the hour hand is on a minute mark, the position of the hour hand is 5X + Y/12, and the position of the minute hand is Y.
On the first occasion, Y = 5X + Y/12 + 6 => 60X = 11Y - 72. Since Y can only take one of the values of 0/12/24/36/48, X = 1 and Y = 12. So the time is 1:12.
On the second occasion, 60X = 11Y - 84 => X = 3 and Y = 24. So the time is 3:24.
3:24- 1:12= 2 hours & 12 minutes