It's good to see that several of my blog friends are still around.
Anyway, I was catching up on all my regular blogs today, when I found this post from Jason. Yes, the man is a geek, but I've got some geekiness in me as well, as I am about to prove to you.
Back in school, maths was always my favourite subject. I loved trying to solve a problem, and battling till I found the answer. A friend of mine's dad was a professor of maths, so his dad was always finding maths problems in everyday life. One day, my friend shared one of his dad's many maths problems with a few of us. It took me about 2 hours, but I cracked it in the end. This was 14 years ago. Anyway, today, I was talking with my cousin who's doing A Level maths, and I wondered if I still had it. So I got a pen and paper, and tried to solve the problem again. Anyway, here we go:
As they sat at lunch, my friend's dad looked at the clock and it was 9pm. He then asked his son the following question:
"Right now, the angle between the hour hand and the minute hand is 90 degrees. When next will it be 90 degrees"
(In the real story, it was dinner, and it was 9pm. But I decided to use 3pm, not that I remembered the answer or the solution, but just to make sure I did it from scratch.)
So, let's begin. First of all, this is probably not the fastest way to the answer, but it was the best I could do in 20 minutes. It took me a lot longer to get the answer as a teenager for the 9pm question, and that involved a quadratic equation, fortunately, I didn't have one of those tonight, as I can't remember how to solve them :)
OK, so let's look at the clock. Both hands are constantly moving.
The minute hand is moving the fastest, 360/60 = 6 degrees a minute
The hour hand moves between each number in an hour. That's 360/12 = 30 degrees an hour= 0.5 degrees a minute.
Armed with this info, let's look at our problem.
Visually, you can see that the time this will occur will be a few minutues after 3.30.
Let's say the number of minutes after 3 o'clock is x.
At that point, the minute hand would have moved 6x degrees from the top (number 12 on the clock face). Let's call this value a.
The hour hand would have moved 0.5x degrees from the number 3, or 90+0.5x degrees from the number 12. Let's call this value b.
So we have :
a = 6x
b=0.5x + 90
Since we know the angle between both hands is going to be 90 degrees, in other words
a-b = 90
6x-0.5x = 180
x= 180/5.5 = 32.72727277272
So the answer is at 43.6 seconds after 32 minutes past 3, the angle between the hands is exactly 90 degrees.
Wow, how sad am I, this is what I'm doing on a saturday night...........lol