For what it is worth, this question was found on the IB Exam of this year.
It is stated in part b of the question that Peter is moving with uniform
motion wrt Jane.
part c asks for derivatio0n of the time dilation equation based on light
clocks
part d asks the question Mark originally posted.
It is clear to me (naively I am sure) that the intention is to apply the
time dilation equation just derived.
Ken Fox
AP/IB Physics Teacher
Smoky Hill High School
Aurora, CO