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Watch the Clock

Age 7 to 11 Challenge Level:

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 wrote:

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 minute.
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 equal
$= 120\div11$
$= 10$ min$+10\div11$ x $60$ sec
= $10$ min $55$ sec (to the nearest second) after 2:00

Isobel sent in her suggestion as:

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.