1. solution: suppose that between 6 o'clock and 7 o'clock on the clock face, the hour hand and the minute hand coincide as 6 o'clock x minutes, the hour hand walks 0.5 degrees per minute, and the minute hand walks 6 degrees per minute; According to the question, it means 6X-0.5X-6*30=0.

The solution is: X=32 8/ 1 1.

The instant hand and minute hand coincide at 6: 32 8/ 1 1.

2. Solution: The hour hand goes 0.5 degrees per minute, and the minute hand goes 6 degrees per minute. When the minute hand and the hour hand are in a straight line between 7 o'clock and 8 o'clock, it is set at 7 o'clock x minutes. According to the question, it means: 6X-0.5X-5*30= 180.

Solve the problem, X=5 5/ 1 1 min. When the minute hand coincides with the hour hand between 7 o'clock and 8 o'clock, it is set at 7 o'clock y. According to the meaning of the question, it is 6Y-0.5Y-7*30=0.

Solve it and you get: Y=38 2/ 1 1 minute.

Xiaoming's problem-solving time * * *: y-x = 38 2/11-5 5/11= 32 8/1minute.

It took Xiaoming 32 8/ 1 1 minute to solve the problem.