To explain special relativity (in chapter 5 titled "the theory of everything"), Hawking starts with an example involving a flying jet, its passenger (being an observer) and an observer on the earth.
He considers the experiment in which a pulse of light travels from the tail of the plane to its nose. In this case, according to the observer on earth, the light has traveled a longer distance than the distance perceived by the jet's passenger. Now, to the jet's passenger, the light has traveled at a normal speed, while to the observer on the ground, if it weren't for the magic of special relativity, the light would have propagated at a faster than normal rate. Specifically, it is argued that special relativity solves the issue by getting the pulse to seem (to the on-earth observer) to have reached the nose of the jet after a longer period of time than what was perceived by the jet's passenger. Thus, for the people on earth, time on the jet seems to be slower.
The obvious question that the book fails to ask, however, is what happens if we consider a pulse of light moving in the opposite direction i.e. from the nose of the jet to its tail. In this case, based on the reasoning above, to the observer on earth, time on the jet has to be perceived as running faster (instead of slower) than normal, resulting in a logical conflict.
Am I missing something here, or is the explanation flawed?