The clock
can be an interesting source of mathematical applications. These can be
applications in mathematics and not in other disciplines as we usually find
mathematics being applied.
Begin by
asking someone to determine the exact time that the
hands of a clock will overlap after 4:00 o’clock. Their first reaction to the
solution to this problem will most likely be that the answer is simply 4:20.
When you
remind them that the hour hand moves uniformly while the minute hand moves
faster, they will begin to estimate the answer to be between 4:21 and 4:22.
They should realize that the hour hand moves through an interval between minute
markers every 12 minutes. Therefore, it will leave the interval 4:21–4:22 at
4:24. This, however, doesn’t answer the original question about the exact time
of this overlap.
You could
show them a technique, once they realize that this is not the correct answer,
since the hour hand does not remain stationary and moves when the minute hand
moves.
The trick: Simply multiply
the 20 (the wrong answer) by 12/11 to get 21(9/11), which
yields the correct answer: 4: 21(9/11).
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