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?
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.
ReplyDeleteTen 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.
How old are they now?
ReplyDeleteTen 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
WHAt????
ReplyDeletehaha!
ReplyDeleteIf anyone answers this, I'll praise him!
I'll ask my teacher and let's see if she can answer this...
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?
ReplyDeleteMy daughter showed me this problem and I thought it would be easy but... it ended up taking me enough time and frustration that I made 4 youtube math videos explaining it in detail! Here is the link to the first video:
ReplyDeletehttps://youtu.be/K4AmpmygNN4
video 1, first paragraph: https://youtu.be/K4AmpmygNN4
ReplyDeletevideo 2, second paragraph: https://youtu.be/_45JDvRsqhA
video 3, third paragraph: https://youtu.be/yImjqBL57rY
video 3, solving the 3 equations: https://youtu.be/iawIP2I-QJU