Step-by-step Solution:

To find when the clock hands coincide between 3 and 4 o'clock:

The relative speed of the minute hand with respect to the hour hand is 5.5 degrees per minute.

At 3 o'clock, the hour hand is at 90 degrees, so the minute hand must gain 90 degrees to coincide.

Time = initial separation / relative speed = 90 / 5.5 = 180/11 minutes = 16 4/11 minutes past 3 o'clock.

Answer: 16 4/11 minutes past 3 o'clock