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It is now between 10:00-11:00 o'clock, and six minutes from now,
the minute hand of a watch will be exactly opposite the place where the hour hand
was three minutes ago. What is the exact time now?
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Imagine wall clock and its clock face.
I will measure degrees in clockwise direction, starting from position 12:00
(from direction vertically up).
Let "m" be the number of minutes after 10:00 under the problem's question
(notice that under this consideration, "m" is not necessary integer number: it can be a real number, actually).
The angle for the hour hand 3 minutes ago from now was 300 + = 300 + degrees.
The angle for the minute hand 6 minutes from now will be degrees = 6(m+6) degrees.
Our equation to find "m" is
300 + = 180 + 6(m+6).
Simplify
600 - 360 = 12(m+6) - (m-3)
240 = 12m + 72 - m + 3
240 = 11m + 75
240 - 75 = 11m
165 = 11m
m = 165/11 = 15 minutes.
ANSWER to the problem's question is 15 minutes after 10:00, or 10:15.
Solved, explained and completed.
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To see many other similar and different clock hand problems, look into the lessons
- Clock problems
- Advanced clock problems
in this site.
Learn the subject from there.