There is a circular clock.
There is a scale showing the “minutes” which divided the circumference into 60 equally in the dial plate.
(1) Choose all the cases where both the hour hand and the long hand have indicated the scale among the following time.
①0:15 a.m. ②2:36 a.m. ③4:44 a.m. ④8:03 a.m. ⑤10:12 a.m.
Furthermore, the 3rd hand (it is not the second hand) that rotates with fixed speed is supposed.
The center of rotation and the direction of this hand are the same as the hand of the clock.
Answer the following questions.
(2) At a certain time in a.m., the 3rd hand pointed a certain scale.
At this time, the hour hand pointed the 12th scale counterclockwise from the 3rd hand.
Moreover, the long hand pointed the 12th scale clockwise from the 3rd needle.
Find this time.
(3) Afterward at a certain time within 12 hours of the time of (2), the 3rd hand pointed a certain scale.
At this time the hour hand pointed the 12th scale clockwise from the 3rd hand.
Moreover, the long hand pointed the 12th scale counterclockwise from the 3rd hand.
Find this time.
(4) Between the time of (2) and (3), the 3rd hand passed the hour hand 10 times.
Find the time for one time rotation of the 3rd hand.