Answer
The films will begin simultaneously (again) at 11:48 AM.
Work Step by Step
The films both begin at 9:00 AM. One goes for 42 minutes, the other is 56 minutes. This is a least common multiple problem. The least common multiple of 42 and 56 is 168. So, 168 minutes after 9:00 AM the films will both begin again at the same time. This would be 11:48 AM
Another way to look at this:
Film A starts at: 9:00 AM, 9:42 AM, 10:24 AM, 11:06 AM and 11:48 AM (start times are every 42 minutes)
Film B starts at 9:00 AM, 9:56 AM, 10:52 AM, 11:48 AM (starts over every 56 minutes)
