between 12 o' clock and 1 o' clock, when will the hands of a clock be together again
The hands of the clock will be together again at about 1:05:27 (1 hour, 5 minutes, 27 seconds past 12).
Quick Scoop
Between 12 o'clock and 1 o'clock, the hour and minute hands meet exactly once, a little after 1:05.
Here’s the clean way to see it:
- The minute hand moves 360 degrees in 60 minutes, so 6 degrees per minute.
- The hour hand moves 360 degrees in 12 hours, i.e., 0.5 degrees per minute.
- The minute hand therefore gains on the hour hand at 6−0.5=5.56-0.5=5.56−0.5=5.5 degrees per minute.
- To be together again after 12:00, the minute hand must gain a full 360 degrees on the hour hand.
- Time taken =360/5.5=720/11=360/5.5=720/11=360/5.5=720/11 minutes =65511=65\tfrac{5}{11}=65115 minutes, which is 1 minute past 1:05 plus about 27 seconds.
So the exact time is:
1 hour 511\tfrac{5}{11}115 minutes after 12:00, i.e., 1:05:27 (approximately).
Tiny Story-style Intuition
Imagine the hands starting perfectly together at 12:00. The minute hand sprints ahead while the hour hand strolls slowly forward. After a bit more than an hour, the minute hand has done almost a full lap and finally “catches up” to the hour hand again just after 1:05, at about 1:05:27.
Key Fact Table (clock-hand overlap)
| Quantity | Value |
|---|---|
| Relative speed (minute vs hour hand) | 5.5 degrees per minute | [3]
| Angle to gain | 360 degrees | [5]
| Time between overlaps | $$ \tfrac{720}{11} $$ minutes ≈ 65.4545 minutes | [1][9][5]
| Time after 12:00 for next overlap | About 1:05:27 | [9][1]