The looking glass was melting away, just like a bright silvery mist. In another moment Alice was through the glass, and had jumped lightly down into the Looking Glass Room. “They don’t keep this room so tidy as the other,” she thought to herself.
Alice began looking about, and was pleased to find that there was a real fire in the fireplace, blazing away as brightly as the one she had left behind. The clock on the chimney-piece was still there, too, but everything about it was completely reversed. Despite being the exact opposite to the one in her own house, however, the looking glass clock displayed exactly the same time.
All of the hours on the clock face were indicated by the same mark, and both hands were the same in length and form. It had been between 6 and 7 o’clock when Alice had passed through the glass.
What was the time to the nearest second? Or when Alice had passed through the glass, it was how many seconds after 6 o’clock? Round your answer to the nearest integer.
Hint: This question is about an analog clock. All of the hours on the clock face were indicated by the same mark. It had two hands, the hour hand and the minute hand. Both hands were the same in length and form. The time was between 6 and 7 o’clock. The clock and its mirror image are exactly the same.
Here we know that the mirrored time is the same as the actually time, and it's between 6 and 7.
So the possible time here is 6:30. And it's 180 secs after Allice had pass through the glass.
Is this what we are looking for here? I feel like I might not be understanding the question right.
Could someone please check my answer? Thanks!
Best Answer
The angle that the hours hand makes with the $12$ o'clock mark is
$H = 30(h + m / 60 + s / 3600 )$
to simplify the problem, we can take $s = 0$ and include the seconds with the real value of $m$ (i.e. $m$ is not an integer)
The angle that the minutes angle makes with the $12$ o'clock mark is
$M = 6 m $
since $h = 6 $ , then
$ H = 180 + m / 2 $
and we want
$ H - 180 = 180 - M $
hence,
$m/2 = 180 - 6 m$
which gives
$m = \dfrac{180}{6.5} = 27.6923 $
which is $ 27 $ minutes and $ 41.54 $ seconds.