How many minutes after 300 PM will the minute hand of the clock overtakes the hour hand?

At 3:00 PM, the hour hand is at the 3 mark, which is 90 degrees from the 12 mark. The minute hand moves at 6 degrees per minute, while the hour hand moves at 0.5 degrees per minute. To find when the minute hand overtakes the hour hand, we set the equation for their positions equal: (90 + 0.5t = 6t). Solving for (t), we find that the minute hand overtakes the hour hand 16.67 minutes after 3:00 PM, or approximately 16 minutes and 40 seconds later.