Clock Problem

Problem
What time after 7:00 o’clock will the hands of a continuously driven clock are together?
 

Problem
Between 3:00 and 4:00, Kathryn looked at her watch and noticed that the minute hand was between 5 and 6. Later, Kathryn looked again and noticed that the hour hand and the minute hand had exchanged places. What time was it in the second case?
 

Problem
What time between 2 and 3 o’clock will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o’clock mark?

A. 2:18:27.6
B. 2:16:00.0
C. 2:17:56.3
D. 2:19:03.1
 

There are 12 dial units in the clock. Every time the minute hand completes 12 dials, the hour hand moves 1 dial. Thus, if the minute hand moves by x the hour hand moves by x/12.
 

Key equations:

The following is an attempt to classify the verbal problems.
 

Number-related problems
Number-related problems are considered as the most basic type of verbal problems. It is taken as the base point of analysis for more complex type of problems.
 

Digit-related problems