= 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,
$$
\boxed{\tau_A=\frac{12}{5}+\frac{26}{7}\frac5{13}
=\frac{134}{35}\,\mathrm{yr}\simeq3.8286\,\mathrm{yr}.}
$$
\b[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.
Back to article page
