Apace means quickly — something is moving or happening at a fast pace. Work can go apace; news can spread apace; change can continue apace. It is not how people talk in a shop or a classroom. You will meet it in books, headlines, and a few set phrases, where the writer wants a slightly old or grand sound. A student who says “I walked apace to school” would sound strange; we just say fast or quickly. Though actually, the old French it comes from meant “at a pace,” which could be quick or slow; English kept the fast reading and left the slow one behind. Today the word almost always sits on progress — building, spreading, growing — not on a person running.