Final answer:
To determine when two signs flashing at different intervals will flash together again, we find the least common multiple (LCM) of their flashing intervals, which for 8 and 12 seconds is 24 seconds.
Step-by-step explanation:
The problem presented involves finding a common multiple of two numbers, which is a mathematics concept typically covered in middle school. In this case, the two numbers are the intervals at which two welcome signs flash: every 8 seconds and every 12 seconds, respectively.
We are looking for the least common multiple (LCM) of 8 and 12 to determine how many seconds will elapse before the two signs flash together again.
To find the LCM of 8 and 12, we list the multiples of each number until we find the smallest number that appears in both lists:
- Multiples of 8: 8, 16, 24, 32, ...
- Multiples of 12: 12, 24, 36, ...
We can see that 24 is the smallest number that appears in both lists, which means 24 seconds is the time interval at which the two signs will next flash at the same time.