Solution:
2hr 11min
Explanation:
Now this question cannot be solved unless you know a fact i.e. the hour hand is exactly on the minute mark five times every hour - on the hour, 12 minutes past hour, 24 minutes past hour, 36 minutes past hour and 48 minutes past hour.
Denoting the number of hours with X and the number of minutes as Y, let us begin with the calculation.
When we have the hour hand on the minute mark, the position of hour hand:
5X + Y/12
And the position of the minute hand = Y
When the first observation was taken,
Y = Y = 5X + Y/12 + 6
Or, 60X = 11Y - 72.
With the given facts, we know for sure that Y can only be 0, 12, 24, 36 or 48.
According to which, the possible values for X and Y can be 1 and 12 respectively. Thus the time must be 1:12 when the first observation was taken.
Similarly, in the second observation, let's make the equation:
60X = 11Y - 84
Here, the possible values for X and Y here are 3 and 24 respectively. According to this, the time is 3:24 for sure.
From 1:12 to 3:24, two hours and eleven minutes have passed.