1. Ten years from now Tim will be twice as old as Jane was when Mary was nine times as old as Tim.

2. Eight years ago, Mary was half as old as Jane will be when Jane is one year older than Tim will be at the time when Mary will be five times as old as Tim will be two years from now.

3. When Tim was one year old, Mary was three years older than Tim will be when Jane is three times as old as Mary was six years before the time when Jane was half as old as Tim will be when Mary will be ten years older than Mary was when Jane was one-third as old as Tim will be when Mary will be three times as old as she was when Jane was born.

How old are they now?

## Wednesday, July 11, 2007

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this is absurd...

ReplyDeletesame

DeleteI think this might be beyond the casual questions I usually pose here.

ReplyDeleteHint: Clue 1 can be reduced to

T is the year Tim was born. J is the year Jane was born. M is the year Mary was born. N is Now.

N + 10 - T = 2*(X - J)

where

X - M = 9*(X-T)

X is the unknown time when the second part of the statement is true.

Keep setting up the algebra like that and you'll get enough equations to solve the puzzle.

Or you could always start guessing numbers and see what works. That could take a while, though.

Ok, I wrote a system of 12 equations to solve this (don't worry, I didn't solve it by hand), and I got a 3/2 in there somewhere for one of the time intervals that was referenced, so I'm not sure if that is right (I expected everything to be integers). I ran the clues through my head with those values, and it works.

ReplyDeletebut I got:

Jane - 8

Mary - 15

Tim - 3

also, mike, I disagree with your sample equation. how can you have a variable representing "now"? my first equation was:

ReplyDeleteT+10 = 2(J-X)

For me, it was easier to figure out their ages by looking at the year they were born and 'now'. So Now is this year.

ReplyDeleteFor instance, Now + 10 - Tims birth year is what I was going for on the left hand side of my first equation.

Very impressive work, abe. I wasn't sure anyone would take the time to do this puzzle.

ReplyDeleteTim is 3

Mary is 15

Jane is 8

hello im a bit late on this but may you tell me your thought prossess

ReplyDelete