A $20-$volume encyclopedia is placed on a bookshelf in numerical order. Each volume is $2$ inches thick, including the front and back covers. Each cover is $\frac{1}{4}$ inch thick. The volumes are placed on the shelf so that the front cover is on the right side of each volume and the back cover is on the left side of each volume. A bookworm eats straight through the encyclopedia, beginning inside the front cover of the first volume and ending after eating through the back cover of the last volume. How many inches of book did the bookworm eat?