Emma owns a cat based on the information given in the text. The statement "Emma's pet purrs and has whiskers" clearly indicates that she has a feline pet, as cats are well known for their whiskers and the sound they make when purring. There is no other animal mentioned in the text that would match those characteristics, so the answer is unambiguously that Emma has a cat as a pet. To arrive at this conclusion, I analyzed the relevant part of the passage which states the specific traits of Emma's animal companion. Purring and having facial whiskers are very distinctive features that only apply to cats among the common household pets named here. Dogs, hamsters and the unspecified pet belonging to John and Sarah do not purr or have prominent whiskers like felines do. Additionally, no other animal besides a cat was even hinted at in connection to Emma in the provided information. While the other characters' pets were identified as a dog, cat and hamster respectively, Emma's was described abstractly as "a pet" but with those two identifying features that only match cats. So the evidence definitively points to Emma owning a feline pet. Therefore, the answer to the question, based solely on the information in the passage and not adding anything external, is that Emma has a cat. The purring and whiskers make it clear that she is a cat owner and the only conclusion supported by the facts in the text.