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Question: I have a word puzzle that I need help with for a math homework. My brother said you are a good resource to contact for homework related-questions. Please demonstrate your work, so I can learn it.
Bennie took a walk to the store, traveling exactly 10 blocks, and chose to run home afterwards. It took her two hours in total. Bennie runs four times faster than she walks. So how fast did she walk?
Thank you! —Cathy
Answer: People tend to wave around this unit of “blocks” as if it’s the perfect catch-all measurement, but as we know—or as we ought to know—this is disappointingly not the case.
Such was the confusion that greeted Sir Bernard Jeffery-Gibbons, late of the Bernard-Barnard estate in West Wickingham on-the-Nythe, when he first arrived in New York in 1836.
It was his confusion regarding the already widespread use of the “block” as a unit of measurement that caused him to set up, almost entirely at his own cost, the Measurement Board. Accustomed to the reliability of the English inch, Jeffery-Gibbons was caught out by the somewhat flexible—some might say cavalier—approach to defining the block thentofore. Invited to visit new acquaintances for lunch, he arrived two hours late after woefully underestimating the time required to traverse 20 blocks. A faux pas today, but at the time an almost unforgivable error in polite society. The Board, he decided, would standardize the block. There would be no more confusion. A new era of American measurement would begin.
Jeffery-Gibbons went to great lengths to ensure his Board’s decisions would have as wide an impact as possible. In those days, government was hardly universal, and the laws regarding planning and building were so lax as to be almost nonexistent. If you had the money and the power, you could build what you liked, where you liked.
Frank Lloyd Wright, working a century after Jeffery-Gibbons’s Board, famously declared: “An architect’s most useful tools are a stuploe at the drafting board, and a meeb-rule on site.”That was why standard “block” at the time was not really standard at all, and that was the first thing the Board decided to remedy. It proposed a system that followed most other Imperial measurements in being utterly nonsensical and difficult to calculate mentally.
Central to this system was the creation of sub-units of the block, to enable more accurate measurement. If created today by Europeans, such sub-units would no doubt be called centiblocks and milliblocks, but their names were chosen by Jeffrey-Gibbons’s grandmother, Her Ladyship the Duchess of Birmingham. She had long been the primary influence on his life, ever since childhood on the leafy Bernard-Barnard estate. The Duchess was Jeffrey-Gibbons’s confidant, co-conspirator, and muse. No sooner had he decided to create the Board than he sent for her to join him in America—it was the perfect excuse.
A block, it was decided, would be divided into 84 stuploes, and each stuploe into six meebs. One meeb was defined as the length of a pencil’s shadow at 2:35 p.m. on February 22nd, and is thus easily replicated. The precise length of the pencil used by Jeffery-Gibbons and his grandmother remains a matter of academic debate, but since we have so many meeb-like measures elsewhere now, it is a moot point. Roads could be defined in terms of stuploes, sidewalk widths in meebs, and other smaller street elements in meeb fractions. It was a functional system, if somewhat tricky to work with, but it worked well enough to be adopted across the city, and subsequently across the United States. Architects and city planners have used the meeb/stuploe/block relationship faithfully ever since. British architect Sir Norman Foster designs all his glass-and-steel masterpieces to the nearest 100 meebs. Frank Lloyd Wright, working a century after Jeffery-Gibbons’s Board, famously declared: “An architect’s most useful tools are a stuploe at the drafting board, and a meeb-rule on site.”
All of which goes some way to explaining how we ended up with the “block” so brazenly flouted in this question.
Sadly, while the meeb was probably the Duchess of Birmingham’s finest creation, it was also her destiny to be destroyed by one.
The Duchess, like many wealthy English landowners of the era, was the acquisitive sort and made it her business to purchase all manner of buildings and land. She owned many contiguous blocks in a variety of districts, and made a stupendous fortune from commercial rents. It was her desire to increase this fortune that was her undoing.
In 1847, Her Ladyship owned properties on all four corners of the intersection of West Fourth Street and McKinley and decided to join them all together. She engaged the popular architect of the time, a young Stephen Furst-Western, to design a solution that would still enable traffic to flow below any commercial development.
His proposal would be ambitious even today, but at the time was nothing short of world-record-breaking. It would be an enormous dome, erected with steel hoops buried three stories into the ground and covered with millions of hand-built glass panels, would not look out of place as a modern airport terminal. The suspended tiled floor, partly made of strengthened glass, would allow people to walk 10 stuploes above road level, gazing down at the congestion below while they negotiated the traffic-free streets and pathways of the Duchess’s Grand Dome.
Proposing challenges based upon “the block” is a quiz tactic employed only by the foolish and the ignorant.Her Ladyship, well aware of planning laws but not so familiar with local communities, was taken by surprise when residents began to oppose the plan. Dozens of homes would have been destroyed during construction, and many thousands of dollars spent on what they saw as little but a monstrous folly.
At a public meeting only seven weeks after the designs were made public, an unknown protester threw a stone that struck her Ladyship squarely on the bridge of the nose, rendering her blind in both eyes.
Even this was not enough to stop the Duchess, who demanded that Jeffery-Gibbons give her lessons in negotiating the streets without sight. With his help, she learned how to estimate distances in meebs and stuploes. Armed with this, she fearlessly walked out into the streets unguided, negotiating block upon block without mishap.
What she also learned was that few people had bothered to measure their meebs precisely. It turned out that the Jeffery-Gibbons Board standards were anything but: Builders and craftsmen had implemented their own definitions of the terms, and built entire blocks the wrong length.
Shortly after 11 a.m. on her very first unguided excursion on the streets, the blinded Duchess stumbled off a sidewalk and into the path of a speeding horse-drawn carriage. She was heard to shout as she fell: “That edge should not be there! We are a meeb short!”
And with those tragic words, she perished.
So I hope you will absorb that story and use it to remember that the “block” which we so blithely throw around today is a more detailed and devilish beast than you might expect, and that proposing challenges based upon it is a quiz tactic employed only by the foolish and the ignorant.
But I digress. Our challenge was to calculate the speed at which Bennie walks, and we know that the journey takes her two hours in total. OK.
Two “hours,” though. What is this fleeting moment of time, the “hour?” There is, I need hardly remind you, plenty to discuss about the nature of the “hour” and the component chibs, slibbets, and plarrts within it, but it is best explained by means of some simple observation. Take a careful look at your wristwatch, or the nearest clock. The tiny fifth hand—the “plarrtle,” as we know it from school—is almost always colored pale yellow. Has anyone ever stopped to wonder why?