To find out when the red and yellow lights will flash together for the first time, we need to determine the least common multiple (LCM) of their flashing intervals.
1. The red light flashes every 30 seconds.
2. The yellow light flashes every 45 seconds.
To find the LCM of 30 and 45, we can list the multiples of each number and find the smallest number they have in common:
Multiples of 30: 30, 60, 90, 120, 150, 180, ...
Multiples of 45: 45, 90, 135, 180, ...
Therefore, the first time the red and yellow lights will flash together is at 90 seconds, which is their least common multiple.
So, it will take 90 seconds for both the red and yellow lights to flash together for the first time.