It’s no secret at all that the minute hand and hour hand move at different rates, however, there are certain points in their rotation where the hands are at exact opposite points of each other, forming a straight line.
Exactly how many time this happens may pop-up as a question in a math quiz, or even as a quirky conversation starter at a party.
Regardless of where the question comes up, rest assured that after reading this article, you won’t only know the answer, but you’ll have a solution to go with it.
The short answer to how many times an hour and minute hand make a straight line in a day is 22.
In a 12-hour stretch, the hands of the watch find themselves at the exact opposite point of each other 11 times, and since a day is 24 hours, you can see the hands in one of those 11 positions twice a day, giving us 22 times that both hands of the watch form a straight line.
The exact times where the hands are in those positions are as follows:
If you track the time, starting at 12:33, the hands get into this position after an hour and five minutes, and you can only subdivide 12 hours into 11 one hour and five-minute divisions.
There is another, more complicated way to reach this answer that includes a series of different variables to find the times the hands form a 180-degree angle.
While the formula itself may be complicated, it’s really nice seeing how watch and clock faces play a big role in teaching and learning math.
This may be because of how the watch face is an accessible and logical visual representation of time that simply can’t be matched.
Whether this question pops up in a logic test or as a conversation starter, you can rest assured that you can easily answer the question, even including the times in a day where the hands make a straight line.