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## Friday, February 15, 2008

### How Old Are They Now?

This puzzle is meant for all the people who had trouble with age problems during high school algebra. In fact it might finish age problems all together. The next time you are asked to solve a problem about Dick being four times older than Fred was last Thursday, etc., pull this one out of your pocket.

I'm not even sure if this one has a real solution or if it's only meant as a joke, but either way it will keep you busy (and baffled!) for a very long time.

Ten years from now Tim will be twice as old as Jane was when Mary was nine times as old as Tim. 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. When Tim was one year old, Mary was three years older than Tim will be when Jane is three time 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?

Anonymous said...

I don't think the age problem can be solved. There doesn't seem to be a set of ages that work in even the first 2 sentences. It seems a shame to have a puzzle that can't be solved. Try this one. It is similar and it does have a solution.

Ten years from now Tim will be twice as old as Jane was when Mary was three times as old as Tim was nine years ago. Eight years ago, Mary was half as old as Jane will be when Jane is seven years older than Tim will be at the time when Mary will be twice as old as Tim will be two years from now. When Tim was one year old, Mary was one year older than Tim was when Jane was three time as old as Mary was six years before the time when Jane was half as old as Tim will be when Mary will be eleven years older than Mary was when Jane was one-third as old as Tim will be when Mary will be seven times as old as she was when Jane was three years old.

Anonymous said...

How old are they now?

Ten years from now Tim will be twice as old as Jane was when Mary was nine times as old as Tim. 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. When Tim was one year old, Mary was three years older than Tim will be when Jane is three time 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.

Solution: Form twelve equations in twelve unknowns, T, J, M and t0 through t8. Solve for T, J and M.
Let T, J and M be the current ages of Tim, Jane and Mary respectively.

“Ten years from now Tim will be twice as old as Jane was …
T+10 = 2(J - t0)

“when Mary was nine times as old as Tim.
M - t0 = 9(T - t0)

“Eight years ago, Mary was half as old as Jane will be …
M - 8= 1/2 (J + t1)

“ when Jane is one year older than Tim will be at the time …
J + t1 = T + t2 +1

“when Mary will be five times as old as Tim will be two years from now.
M + t2) = 5(T + 2)

“When Tim was one year old, …
T – t3 =1

“Mary was three years older than Tim will be …
M – t3 = T + 3 + t4

“when Jane is three time as old as Mary was six years before the time …
J + t4 = 3(M – t5 - 6)

“when Jane was half as old as Tim will be …
J – t5 = ½ (T + t6)

“when Mary will be ten years older than Mary was …
M + t6 = M + 10 – t7

“when Jane was one-third as old as Tim will be …
J – t7 = 1/3 (T + t8)

“when Mary will be three times as old as she was when Jane was born.”

M + t8 = 3(M – J)

Answer: T = 3, J = 8, M = 15

Anonymous said...

WHAt????

Anonymous said...

haha!

If anyone answers this, I'll praise him!

I'll ask my teacher and let's see if she can answer this...

Anonymous said...

Can someone tell me who the original author of this age problem is? I am a math teacher and would like to include it in my publication. Can you give me permission?