# Homework Help: Find the Youngest Twin in after two travel to different stars at different speeds.

1. Oct 16, 2012

### Kuiper83

1. The problem statement, all variables and given/known data
Two twin astronauts, John and Joe, leave the Earth at the same time for a trip to far away stars. According to their mother, who stays on earth, John reaches a star that is 4 light years away after 5 light years and Joe reaches a star that is 6 light years away after 10 light years. After reaching their destination they return along the same path with the same velocities as their outbound trip. When both twins are back home who will be younger?

2. Relevant equations
Δs^2=(Δct)^2-(Δx)^2
ct'=γ(ct-xv)

3. The attempt at a solution

I used the lorentz transformation in the form of
ct'=γct-βγx
with γ=5/3 and 5/4
and β =3/5 and 4/5
which gave me times of ≈2.6s and 4.45s which means John is younger.

However, while I got the correct temporal relation between the twins I got no credit. Is this because I should have used the proper time/spacetime interval? This was an exam question and I feel like I should have gotten some credit, and so I just wanted to make sure that I had some basis for these claims.