Joe's age, Joe's sister's age, and Joe's father's age sum up to a century.…

Concept: In age-relation puzzles, every clause about 'when someone reaches a certain age' translates into an algebraic statement using the fact that the age difference between two people never changes over time. Combine these statements with the given total to pin down the unknown age.

1. Let Joe's present age be J, his sister's present age be S, and his father's present age be F. The problem gives J + S + F = 100.

2. Let x be the number of years from now until Joe's age equals his father's present age, so x = F − J.

3. At that future time, the sister's age will be S + x. The problem states this equals twice her present age: S + x = 2S, which simplifies to x = S.

4. Combining x = F − J with x = S gives F − J = S, i.e. J + S = F.

5. Substituting J + S = F into J + S + F = 100 gives F + F = 100, so F = 50.

Cross-check: with F = 50, the total-age equation requires J + S = 50, which matches exactly what the doubling condition (J + S = F) demands — both conditions are satisfied simultaneously, confirming the value.

Note on the remaining clue: the problem also describes a further age relationship linking the father's age to a past point when the sister's age matched her father's — that clue fixes Joe's and his sister's individual present ages (their split of the 50 years between them), but it does not change the father's age, which is already uniquely pinned down above by the total and the doubling condition alone.

Hence, the father's present age is 50 years.