Answer:
3 hours from noon, or 3 pm.
Step-by-step explanation:
As of 12 noon, the frequencies are 45 and 60 minutes.
To find out when they leave at the same time again, we need the LCM (least common multiple) of the two frequencies, i.e.
LCM (45, 60) = common time from {45,90,135,180,225,270,315,360....} and{60,120,180,240,300,360,...}
We see that they leave at the same time again at 180 and 360, ... minutes. Since 180 minutes is the least common multiple, 180 is the next time they leave together again, or 3 hours after noon, i.e. 3pm.
Happy New Year, ... en quelques minutes! :)
