Question

A hungry bookworm bores through a complete set of encyclopedias consisting of n volumes stacked in numerical order on a library shelf. The bookworm starts inside the front cover of volume 1, bores from page 1 of volume 1 to the last page of the last volume and stops inside the back cover of the last volume. Note that the book worm starts inside the front cover of volume 1 and ends inside the back cover of volumen Assume that each volume has the same number of pages. For each book, assume that you know how thick the cover is, and that the thickness of a front cover is equal to the thickness of a back cover, assume also that you know the total thickness of all the pages in the book. How far does the bookworm travel? How far will it travel if there are 12 volumes in the set and each book has 3 inches of pages and a 3/8-inch thick cover? The bookworm will travel inches. (Type an integer or decimal rounded to two decimal places as needed.)

Answer 1

Concept:

The bookworm starts from the first page of the first volume by eating the first page and it stops in the back cover of the last volume after eating the last page of the last volume. It means that at the start the head of the bookworm was in touch with the first page of the first volume and ended in the back cover of the last volume where its tail would just cross the last page. Hence, the total distance covered by the book worm would not include the front cover of the first volume and the back cover of the last volume.

Solution:

Total distance covered by the book worm = (thickness of pages of first volume + thickness of back cover of the first volume) + (n -2)(front cover + pages + back cover) + (thickness of pages of last volume + thickness of back cover of the last volume)

Total distance covered by the book worm = [3 + (3/8)] + 10[ (3/8) + 3 + (3/8) ] + [3 + (3/8)]

= 44.25 inches (ans)