Can You Be Half Someone's Age More Than Once?

[KingBigness]

Homework Statement

I need a rock solid proof.

Is it possible to be half someones age more than once?

Eg. I was born at 0 while my dad was born at 20, he will be 40 when I am 20 hence I am half his age. Is this possible more than once?

 

[Joffan]

The difference in your ages is fixed. Use that constant to show that the fraction only ever decreases.

(Quibble: in your example, if I die when I'm 30, will I again be half my Dad's age when he turns 60?)

 

[genericusrnme]

You have two ages, which can be represented by functions which are linear in time, what do you know about the solutions to systems of linear equations?