Answer:
Yes, Jack can board the flight.
Step-by-step explanation:
1) Jack's plane is scheduled to take off at 12:05am.
2) The gate closes usually 15 minutes before take-off time.
3) He arrives at the gate at 11:45pm.
Taking a closer look, Jack has enough time to make it.
If the gate does close 15 minutes before take-off, Jack will have 5 minutes to board his flight. So, he will barely make it in time.
12:05 - 11:45 = 20 minutes. :)