Twice the Age Puzzle - Solution

The Puzzle:

Twice the Age
Age problems were quite the fashion in antiquity. Here is an example:

I have twice the age you had when I had the age you have.
When you`ll have the age I have, together we will have 63 years.

How old are we (individually) ?

Our Solution:

The puzzle is about 3 instants in time.

Let`s have P for my age in the past, P` for yours, N for my age now, N` for yours, F for my age in the future and F` for yours.
Then we have:

N = 2P`
P = N`
F` + F = 63
F` = N = 2P`
You can represent it in a timeline to make it clearer if you wish.
The trick here is that time runs the same for both me and you, therefore we can write :

F` - N` = F - N
So: 2P` - P = 63 - 2P` - 2P`
So: P = 63 - 6P`

N` - P` = N - P
So: P - P` = 2P` - P
So: 2P = 3P`

The rest is easy. In the end we have N = 28 and N` = 21.

So we are 28 and 21
Puzzle Author: Fares Arousse

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