Ok I understand. So it is just about precision. And of course for something that is moving far slower than c, you couldn't start the problem with that assumption, (which was what threw me off from the beginning). Thank you very much.
This example is worked out in the book, and at the beginning, they make the assumption that the muon is traveling at c, and then find the change in time from the Earth reference frame using delta t=100km/c. Then delta t is plugged into the time dilation equation on the left side and we solve for...