Answer to maths homework question?

[superFoolish]

It's not my homework; apparently, this came up on Mumsnet recently, and children (and their parents) really struggled with it. It's supposed to be KS2 level (7-8 years old).

The question is:

''On the coast there are three lighthouses.

'The first light shines for 3 seconds then it is off for three seconds. The second light shines for 4 seconds then it is off for 4 seconds. The third light shines for 5 seconds then it is off for 5 seconds. All three lights have just come on together.

a) 'When is the first time that all three of the lights will be off together?

b) 'When is the next time that all three lights will come on at exactly the same moment?'

I solved the problems with a simple chart on a grid, in about 30 seconds; I prefer visual solutions. However, there must be a mathematical solution (presumably relating to factors), and I am assuming that the children to whom the homework was presented, covered this is in their lessons (although, that may not be the case)! Can anyone advise the mathematical solution?

The article that I read (on MSN) is not well-written; perhaps one of the 8 year-olds wrote it, and no mathematical answer has been provided (at least, not a correct one that I can find)!

Below is a link to the article on MSN; there is no link to the original Mumsnet article, and I suspect that the MSN article was syndicated from elsewhere:

https://www.msn.com/en-au/lifestyle/sma ... ar-AAxdLD3

[DrBunsenHoneydew]

The first question is easiest done by a simple diagram of on and off - far simpler than trying to calculate it in some way.
The second is the Lowest Common Multiple of the three complete cycles (6, 8 and 10 seconds).

[GoSeigen]

It's not my homework; apparently, this came up on Mumsnet recently, and children (and their parents) really struggled with it. It's supposed to be KS2 level (7-8 years old).

The question is:

''On the coast there are three lighthouses.

'The first light shines for 3 seconds then it is off for three seconds. The second light shines for 4 seconds then it is off for 4 seconds. The third light shines for 5 seconds then it is off for 5 seconds. All three lights have just come on together.

a) 'When is the first time that all three of the lights will be off together?

b) 'When is the next time that all three lights will come on at exactly the same moment?'

I solved the problems with a simple chart on a grid, in about 30 seconds; I prefer visual solutions. However, there must be a mathematical solution (presumably relating to factors), and I am assuming that the children to whom the homework was presented, covered this is in their lessons (although, that may not be the case)! Can anyone advise the mathematical solution?

The article that I read (on MSN) is not well-written; perhaps one of the 8 year-olds wrote it, and no mathematical answer has been provided (at least, not a correct one that I can find)!

Below is a link to the article on MSN; there is no link to the original Mumsnet article, and I suspect that the MSN article was syndicated from elsewhere:

https://www.msn.com/en-au/lifestyle/sma ... ar-AAxdLD3

For that age group I can't imagine they were reqired to solve it any way but graphically. It's a test of their ability to represent time on an axis surely?

Another way is to use logical reasoning, which is also mathematics of course, whence the answers are 5 seconds and 24 seconds respectively -- for an adult, quicker than the graphical method. The first answer is obvious; an easy solution to the second problem involves thinking about the times that the third light is on, then using multiplication tables / common multiples to determine when the second and first lights also come on (every 6/8 seconds respectively).

EDIT: Didn't read b correctly (24 seconds is the first time they are all on at the same time), but as the previous poster said, they will tun on simultaneously at the lowest common multiple of their periods, i.e. 2x2x2x5x3=120 seconds.

GS

[DrBunsenHoneydew]

Your second answer is not quite right. You have answered the time when all 3 lights happen to be next on simultaneously, but the question actually asks when they “come on” at the same moment.

[PinkDalek]

Not sure a graph is needed. Using the 3rd light, which comes on every 10 seconds:

1. 10, 20, 30, 40, 50, 60, 70, 80, 90 etc gets to 120 secs which is divisible exactly by 6, 8 & 10.

2. The next being 240 secs I think.

I imagine that age could get there in their heads.

[GoSeigen]

Not sure a graph is needed. Using the 3rd light, which comes on every 10 seconds:

1. 10, 20, 30, 40, 50, 60, 70, 80, 90 etc gets to 120 secs which is divisible exactly by 6, 8 & 10.

2. The next being 240 secs I think.

I imagine that age could get there in their heads.

A graph is not needed but is probably what is intended for seven-year-olds.

Interesting that the mums and dads missed the point about the graphical method too. Time is a continuous quantity not discrete, so it is simpler to draw a continuous graph -- rather than a discrete one as many of them tried to do, getting confused and arriving at the wrong answer in the process!

GS

[PinkDalek]

I’m on my mobile and didn’t read the article nor your (edited) reply. Looks like I misread the first question as on not off!

[superFoolish]

Thanks for the responses; I went for the graphical method because:

a) It's the way my brain works most effectively, and
b) Having taught children aged 11-17 (not maths), I was (most likely incorrectly) guessing that was the expected method.

There was absolutely no context to the question, no indication of ability, etc.

It's interesting to note that, both in the article that I linked to, and in the responses to my OP, there was quite a bit of misreading of the question. I'm not pointing fingers! I suspect most (including me), were viewing this out of interest, and multi-tasking, rather than assisting a 7/8 year-old to do their homework!