If a 6'8" foot long piece of wood is cut so that one piece is one-fourth the size of the other, how long will the longer piece be, in feet and inches?

To solve this puzzle, the first step is to convert the total length of the wood into a single unit, which makes the division much easier. Since there are 12 inches in a foot, a 6-foot-8-inch piece of wood is equivalent to 80 inches in total. The problem states one piece (Review) is one-fourth the size of the other, which means you can think of the wood as being made of five equal parts: four for the longer piece and one for the shorter. Dividing the total length of 80 inches by these five parts gives you 16 inches for each part. The longer piece consists of four of these parts, so its total length is 64 inches, which converts back to 5 feet and 4 inches.

The units of feet and inches used in this problem have a long and fascinating history. For much of human history, these measurements were not standardized and could vary significantly from place to place. The length of a "foot" could range from 9 to 16 inches, often based on the actual foot size of a local ruler, like King Henry I of England. Similarly, the inch was once defined by the width of a man's thumb or, more precisely by a 14th-century English king, as the length of three dry, round grains of barley laid end to end.

This lack of a consistent standard made trade and construction difficult. Imagine buying a "foot" of lumber in one town, only to find it was a different length in the next. The eventual standardization of these units was a crucial development for commerce and science, ensuring that a foot in one part of the world was the same as a foot anywhere else. This process of creating uniform measurements, like the metric system used by most of the world today, allows for the precise calculations needed in everything from simple woodworking projects to complex engineering feats.