Just to recap, here was this week’s puzzle:
“How many minutes is it before 12 noon if nine minutes ago it was twice as many minutes past 10 am?”
The solution is after the break.
For today’s answer, I’m actually going to copy Xbalanque’s explanation from the comments of the original puzzle post, with one or two amendments to make it easier to follow for anyone not into maths, because he did it much more smoothly than me! I’ve added comments underneath each line of algebra, too:
Let 0 = 10 am and let x be an integer (whole number), so that, for example, if x = 7, then we are discussing 10:07 am (x + 0).
2(120-x) = x-9.
As you can probably see, the 120-x is the number of minutes we want to find subtracted from the two hour time gap between 10 am and 12 noon, and it’s doubled because 9 minutes ago, it was twice as many minutes past 10 am. The 9 minutes ago gives us the x-9 part.
240-2x = x-9
Multiply out the bracket.
249 = 3x
Add 9 to both sides of the equation, and then add 2x. Doing this removes all the negatives. Then, divide by 3 to leave…
x = 83.
So, x + 0 is 11:23 am. Therefore, it’s 37 minutes before noon.
Well done to everyone who solved the puzzle, and if you didn’t, better luck next week!
Vel.
der Hexenmeister 
October 23, 2009 at 11:14 pm
Neat solution. I admit I didn’t actually bother this week, but I did think about it briefly on the bus and this was the method I thought would probably do it. Unfortunately, I lacked my trusty Back-Of-The-Envelope (R) 😛
Of course trial and error would do it, but not as fun!