Final answer:
The answer involves finding the Least Common Multiple (LCM) of 17 and 15, which is 255 seconds. This is the time after which both the red and green lights will flash together.
Step-by-step explanation:
The question asks after how many seconds will a red light flashing every 17 seconds and a green light flashing every 15 seconds both flash at the same time again. To solve this, we need to find the Least Common Multiple (LCM) of the two time intervals. The LCM of 17 and 15 is the smallest number that is a multiple of both 17 and 15.
First, list a few multiples of 17 (17, 34, 51, 68, ...) and 15 (15, 30, 45, 60, ...), and then find the smallest number that appears in both lists. In this case, the LCM of 17 and 15 is 255. Therefore, both the red and green lights will flash together every 255 seconds.