Answer: 60 minutes or 1 hour.
Step-by-step explanation:
Since one moderator was typing every 20 minutes while the other moderator was typing every 30 minutes, then the time the other one will find about the insult simply means that we should find the lowest common multiple of 20 and 30. This will be:
20 = 20, 40, 60, 80, 100, ..
30 = 30, 60, 90, 120 .....
Here, we can see that the lowest common multiple is 60. Therefore, the other one will find about the insults in 60 minutes.