If the clock goes from 2:30 to 2:55, what angle does the hour hand and minute hand turn

If the clock goes from 2:30 to 2:55, what angle does the hour hand and minute hand turn

It takes 12 hours = 12 * 60 = 720 minutes to walk a circle (360 °) clockwise, and the speed of real-time needle is 360 / 720 = 0.5 ° / minute;
It takes 1 hour to walk 360 degree, and the speed of instant needle is 360 / 60 = 6 degree / min
So when the clock goes from 2:30 to 2:55, both the hour hand and the minute hand go for 25 minutes,
So the hour hand turns 0.5 * 25 = 12.5 ° and the minute hand turns 6 * 25 = 150 °

When does the hour hand and minute hand form a 90 degree angle between 2 o'clock and 3 o'clock
fast

At 2 o'clock, the angle of the hour and minute hand is 60 degrees
Every minute, the angle difference is 6-0.5 = 5.5 degrees
So after (60 + 90) △ 5.5 = 150 / 5.5 = 300 / 11 minutes, it will form a 90 degree angle

In the afternoon, when the hour hand and minute hand of the clock coincide and the second hand is around 49 seconds, how much time does the clock indicate (accurate to seconds)?

Every time the hour hand and minute hand overlap, it needs: 12 △ (12-1) = 1211 hours = 1 hour 5 minutes 27311 seconds. So the first overlap is 1:5 minutes 27311 seconds, the second is 2:10 minutes 54611 seconds, the third is 3:16 minutes 21911 seconds, and the fourth is 4:21 minutes 49111 seconds (meet the requirements), so the answer is 4:21 minutes 49 seconds in the morning or 4:21 minutes 49 seconds in the afternoon The time is 4:21:49 a.m. or 4:21:49 p.m