Answer
(a) Equal. (b) Choice III
Work Step by Step
(a) We know that the rotational period of Jason is equal to the rotational period of Betsy because it takes the same amount of time for the merry-go-round to complete a revolution for all points on the merry-go-round.
(b) We know that the best explanation is option (III) -- that is, it takes the same amount of time for the merry-go-round to complete a revolution for all points on the merry-go-round.