This challenge caused a lot of hard thinking.
Some took the time to be around 2.10 and others around 3.15
according to how they interpreted the question. Either way led to
some careful working out. The amount the small hour hand moves led
to slightly different suggested answers.
Hasa, Javeria and Sarah
First we estimated an answer. The answer must be between 2 and 3 on
the clock. So it must be between 2:10 and 2:15. Then we worked out
how many degrees each hand moves in 1 minute.
The minute hand moves $360\div60=6$ degrees per minute.
The hour hand moves $(360\div12)\div60=0.5$ degrees per
If $T$ is the time in minutes after 2:00 then the minute hand has
moved $6T$ degrees.
The hour hand has moved $60+0.5T$
When the hands are pointing in the same direction these must be
$= 10$ min$+10\div11$ x $60$ sec
= $10$ min $55$ sec (to the nearest second) after 2:00
Isobel sent in her suggestion
I found out that roughly the answer was 3:17 am. I found this
puzzle quite tricky. So I borrowed my mum's alarm clock and fiddled
with the arms until I found the answer.