In order to answer this question you must read the book, but my answer (meaning don't copy paste change a few things) is:
In Act I of The Phantom Tolbooth the time plays an important role, the Clock says, "Time is important, but it's what you do with it that makes it so." The author thinks you need to take advantage of time and use it wisely. The characters the Whether man and the Watchdog are both examples of characters that take advantage of time.
The Whether man is an example of a character that illustrates the author's point of view which is that you should take advantage of time and use it wisely. The Whether man has a job to do, and he does it well. His career is to hurry people beyond expectations whether they like it or not.
The Watchdog is another character that values time. In the story, he says, "KILLING TIME? It's bad enough wasting time without killing it." This quote shows how much the author and the watchdog don't like wasting time. His job is to sniff around to make sure nobody is spending time.
The lethargarians although they appear to do nothing, they are always following their schedule thus not wasting time.
In conclusion, the characters the Whether man, watchdog, and even the lethargrians illustrate how to take advantage of time.
