Problem of the Week 3

Suppose a metric clock uses the following system:

What is the time in our system when the metric clock registers 4 hours, 5 minutes, 6 seconds, and 7 mini-seconds?

 

Alternate Problem 3

Between twelve o’clock midnight and twelve o’clock noon, how many times are the minute hand and hour hand of a clock at right angles to each other.

 

Extension Problem 3

The minute hand and hour hand of a clock are together at exactly twelve o’clock.

How many times do the hands coincide in a twelve-hour period?

At what time after twelve o’clock do they next coincide?

If the hour, minute, and second hands coincide at exactly twelve o’clock, at what time will all three next coincide?