Past exam of the physics 1 paper of the University of Oxford / 2017 resit / 10 / c / Solution

Alison's outbound proper time is $(13/5)(12/13)=12/5$ years. Her return Earth-frame duration is $T-13/5=26/7$ years, with time dilation factor $\sqrt{1-(12/13{)}^2}=5/13$. Adding the two segments,Alison is two years younger than Belinda at reunion. Her turnaround changes inertial frames, and the faster return segment accumulates less proper time per unit Earth-frame time. The twin paradox is resolved by comparing the complete worldlines, not by applying one constant time dilation factor to Alison's whole journey.