Hour hand, minute hand and second hand

Answer the following questions about the hour hand (short hand), the minute hand (long hand) and the second hand of the clock in 60 minutes from 10:10 to 11:10.

(1) Find the time when an hour hand and the minute hand overlap. The second only should answer using a fraction.

(2) Considering the case that any two of three hands do not have overlapped either among three hands, an hour hand, the minute hand and the second hand.

In this case, the center of the clock is divided into three angles as shown in a figure.

Find the number of times that two angles become equal among these from the time when it is found at (1) until 11:10 and also find the last time when two angles become equal.

As for the time, the second only should answer using a fraction.

Answer