Question

calculate time to describe 45° by the hour hand of clock​

Answer 1

Answer:

First notice that for every hour between 0:00 am and 23:59pm, there can be at most two time instances where the angle is 45. For every hour, we can form an equation:

1. At hour 0, assume it is x minutes passed 0 where x is not limited to an integer, then the minute leg has moved 6x degrees and the hour leg has moved 0.5x degree. Then we have:

6x - 0.5x = 45

or

360-6x + 0.5x = 45

2. At hour 1:

6x - (30*1+0.5x) = 45

or

360-6x + (30*1+0.5x) = 45

3. At hour 2:

(30*2+0.5x) - 6x = 45

or

6x - (30*2+0.5x) = 45

4. At hour 3:

(30*3+0.5x) - 6x = 45

or

6x - (30*3+0.5x) = 45

5. At hour 4:

(30*4+0.5x) - 6x = 45

or

6x - (30*4+0.5x) = 45

6. At hour 5:

(30*5+0.5x) - 6x = 45

or

6x - (30*5+0.5x) = 45

7. At hour 6:

(30*6+0.5x) - 6x = 45

or

6x - (30*6+0.5x) = 45

8. At hour 7:

(30*7+0.5x) - 6x = 45

or

6x - (30*7+0.5x) = 45

9. At hour 8:

(30*8+0.5x) - 6x = 45

or

6x - (30*8+0.5x) = 45

10. At hour 9:

(30*9+0.5x) - 6x = 45

or

6x - (30*9+0.5x) = 45

11. At hour 10:

(30*10+0.5x) - 6x = 45

or

6x - (30*10+0.5x) = 45

12. At hour 11:

(30-0.5x) + 6x = 45

or

(330+0.5x) - 6x = 45