Is this a Geometric Series?

Algebra Level 3

The hands are together at noon.
The minute hand sweeps around the clock.
By the time the minute hand returns to the 12 o'clock position,
The hour hand has moved to 1 o'clock.
By the time the minute hand advances to the one o'clock position,
The hour hand isn't there anymore.
It has moved just a little, teensy bit...

How long does it take for the two hands on an analogue clock to come together again ?

1 hour, 5 minutes, 30 seconds 1 hour, 5 minutes, 37 seconds 1 hour, 5 minutes 1 hour, 5 minutes, 27 seconds

2 solutions

Chew-Seong Cheong
Jul 18, 2015

The hour-hand and minute-hand meet $11$ times in $12$ hours. Therefore the frequency that they meet is $\dfrac{11}{12}$ per hour and the period between their meetings is $\frac{12}{11}$ hours or $\boxed{\text{1 hour 5 minutes }27 \frac{3}{11} \text{seconds}}$ .

Moderator note:

How can we know that they meet together 11 times in 12 hours?

How do we know that they met regularly and thus the time difference is the average?

Matthew Musick
Jul 18, 2015

I've improved the phrasing of your problem. You were asking for "how often", which could be interpreted as "how many times does this happen in a day".

Calvin Lin Staff - 5 years, 11 months ago

Is this a Geometric Series?

2 solutions

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