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

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It is impossible to be half someone's age more than once due to the fixed age difference between individuals. As one person ages, the fraction representing their age relative to the other continually decreases. The example provided illustrates that when one individual reaches a certain age, they can only be half the other's age at that specific point in time. The discussion also touches on the implications of mortality on age relationships, but the core mathematical principle remains that the age ratio can only occur once. Therefore, the concept of being half someone's age is limited to a singular instance in time.
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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?
 
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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?)
 
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?
 

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