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 Post subject: Flashing beacons
PostPosted: Thu Jun 05, 2008 9:28 am 
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Joined: Thu Jun 05, 2008 9:20 am
Posts: 13
Three roadside flashing beacons are all switched on at the same time. One flashes every 6 seconds, one every 9 seconds and the third every 12 seconds. How many seconds after being switched on do they flash at the time?

I am aware you could do it like this:

6 second beacon: 6, 12, 18, 24, 30, 36
9 second beacon: 9, 18, 27, 36
12 second beacon: 12, 24, 36

Hence answer 36 seconds.

However, I am sure these questions get much harder so that it is impossible to write it out long-winded like this. I know there is a rule for these types of problems but can't for the life of me remember what it is!

Can anyone help?


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 Post subject: Re: Flashing beacons
PostPosted: Thu Jun 05, 2008 10:52 am 
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Joined: Thu Jan 03, 2008 8:26 am
Posts: 1326
Location: Watford, Herts
Here we go again wrote:
Three roadside flashing beacons are all switched on at the same time. One flashes every 6 seconds, one every 9 seconds and the third every 12 seconds. How many seconds after being switched on do they flash at the time?

I am aware you could do it like this:

6 second beacon: 6, 12, 18, 24, 30, 36
9 second beacon: 9, 18, 27, 36
12 second beacon: 12, 24, 36

Hence answer 36 seconds.

However, I am sure these questions get much harder so that it is impossible to write it out long-winded like this. I know there is a rule for these types of problems but can't for the life of me remember what it is!

You want the smallest number that all of these numbers divide into. You could do it by factorizing:
6 = 2x3
9 = 3x3
12 = 2x2x3
so a common multiple must have all these factors:
2x2x3x3 = 36


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 Post subject:
PostPosted: Sun Jun 08, 2008 10:58 am 
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Joined: Tue Jan 01, 2008 1:05 pm
Posts: 515
Or just multiply 12....... 12, 24, 36 etc, until you come to a number that is divisible by 9 and 6 as well.


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 Post subject:
PostPosted: Thu Jun 12, 2008 9:30 am 
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Joined: Thu Jun 05, 2008 9:20 am
Posts: 13
Thanks for the replies. I think it's probably easiest for a 10 year old to go through the 12 times table and check when they find a multiple of the other numbers then and leave factoring until they are a bit older.


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 Post subject:
PostPosted: Thu Jun 12, 2008 6:06 pm 
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Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11944
If you do the 12 times table 6 is already going to be a factor so you are just looking for a multiple of 9.


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 Post subject:
PostPosted: Fri Jun 13, 2008 1:28 pm 
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Joined: Thu Jun 05, 2008 9:20 am
Posts: 13
Good point. That makes it easier still. Thanks


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