Twice the Age Puzzle - Solution
The Puzzle:
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