It’s 3 O’Clock.
What will be the time when the minute and hour hands are next in the same position (coincident)?
One way to solve this problem: start with the minute hand at the 12 and hour hand at the 3. Let’s call x the number of minute markers from 12 O’clock to where the hands meet. The minute hand will take x minutes to get there (it travels a minute marker a minute). The hour hand will need to travel (x-15) minute markers and we know it will take (x-15)*12 minutes to get there. When the hands meet, the same time will have elapsed for both so we can solve for x:
x = (x-15)*12
x=12x-180
11x=180
x=180/11
x=16 and 4/11 minutes
There’s a smarter way to solve this problem: you realize that there’s 11 intervals at which the minute hand and the hour hand coincide over the course of a 12 hour period, so each is 60/11 minute markers apart on the clock face. The one after 3 O’Clock is the third, so it’s 60*3/11 minutes after the hour, which is 180/11 minutes.
It’s interesting that my algebra teacher spent weeks, if not years getting the class to think like the non-quant. Mechanically, logically, but not efficiently. Imagine if our educational system focused on getting high-schoolers to start thinking like quants from the beginning?
benkster… it’s a good point. I wonder if some people are predisposed to think one way or the other – and how much of it can be taught.
less of the quant worship please! they live in this space. of course they are going to find elegant solutions more quickly.
there’s definitely a predisposition element to this. some people see problems differently. music as math. numbers as a landscape. spinning dancers, etc.
education systems produce lots of bright people that can solve a differential equation if you tell them that’s the topic under test. what they fail to develop is the ability to look at a problems and figure out for themselves what knowledge area to reach into to find a solution. this ability to identify where to start is often key to solving these brain teasers.
btw, love that none of the coding entries have responses!
http://www.news.com.au/perthnow/story/0,21598,22492511-5005375,00.html?from=mostpop
http://www.secamlocal.ex.ac.uk/people/staff/mrwatkin/isoc/twins.htm
getmetheswan – the “quant worship” had a little tongue in cheek to it… though subtle, like all good australian humor.
I like your spinning dancer link – I was stuck on clockwise for a while. It took some effort for a momentary switch to anti-clockwise. So what does this say… I’m a “touchy feely” guy? Are you crazy?
I was stuck on clockwise with no hope of reversing it. Does that qualify me for government assistance?