Recuurence of an event

[sarahenry]

Hi,

 

An event A happens very 13 years

 

Another event happens every 17 years.

 

How to calculate when they happen together again

 

Thanks in Advance

Sara

[mooeypoo]

Is this a riddle or a homework question (IE, should we 'guess the answer', or explain how to try and solve it?)

[raj bhramar]

 

Say event 'A' happens after 13a years and event 'B' happens same day after 17b years.

Obviously 17b must be equal to 13a, which is possible only when a = 17 and b = 13.

So after 13 * 17 = 221 years Both event happens together again.

 

[imatfaal]

And the Cicadas start to fill the evening air with their song!

[BJwojnowski]

they will not occur again in the same material plane. When event A happens 13 years later event B will occur four years after that. event A will occur again twenty six years from the origen and B will occur again in thirtyfour years. If time is linear the difference between the reoccurences will only get larger and larger of course assuming that there is only one frame of reference and the same clock timing both events.

[raj bhramar]

they will not occur again in the same material plane. When event A happens 13 years later event B will occur four years after that. event A will occur again twenty six years from the origen and B will occur again in thirtyfour years. If time is linear the difference between the reoccurences will only get larger and larger of course assuming that there is only one frame of reference and the same clock timing both events.

OP does not say that event B will occur 4 years after event A takes place. Event A occur every 13 years and event B every 17 years. So if today both events occured together, then counting from today, second occurrence of A will be after 13 years from now and that of B will be 17 years from now. Then third occurence of A will be 26 years from now and that of B will be 34 years from now. Thus the difference goes on increasing for every successive occurrence.

[CaptainPanic]

Both events occur in the same year after 221 years.

 

For event A, which occurs every 13 years, that will be the 17th time it occurs since we started counting.

For event B, which occurs every 17 years, that will be the 13th time it occurs since we started counting.

[ewmon]

Sarahenry, these two numbers (13 and 17) are also primes, and so finding the answer mathematically is easier than if they weren't primes. This problem sounds like homework, when leads me to expect that you'll encounter similar but more complicated problems next. For example, Event A recurs every 6 years and Event B recurs every 8 years, or Event A recurs every 3 years and Event B recurs every 9 years. These problems involve finding and using common factors.

[BJwojnowski]

Thank you for clearly stating what I was trying to say.

[John Cuthber]

There is a whole stack of related stuff here

http://en.wikipedia.org/wiki/Least_common_multiple