Optimizing Your Outdoor Space: How Joe's Paved Garden Affects His Daily Walk
Joe has a spacious 40 by 72 ft rectangular yard which he has divided into a pave border and a central grass area. He walks his dog around the inner grass area, which is bordered by a stone pathway. This article explores how the design and layout of Joe's yard impact his daily walk, specifically the number of laps he needs to walk to cover at least a mile. We'll also discuss the importance of stone paving in garden design, and how the shape and layout of the border can influence the number of laps required.
Understanding Joe's Yard Layout
Joe's yard is a 40 by 72 ft rectangle, which equates to 2880 square feet. He paved 5/12 of the area with stone, creating a border around the central grass area. This stone border covers an area of 1201 square feet. The remaining 1679 square feet are dedicated to the central grass area.
The Importance of the Central Grass Area
The central grass area is crucial because Joe walks his dog around this area every morning. To determine the boundary of the central grass area, we calculate its perimeter by taking the square root of the 1679 square feet. This gives us a length of approximately 40.79 feet on one side, which multiplied by four sides results in a total perimeter of about 163.2 feet.
Calculating Laps to Walk a Mile
Now, let's tackle the question of how many laps Joe needs to walk to cover at least a mile. One mile is equivalent to 5280 feet. To convert this into laps, we divide 5280 feet by the perimeter of the central grass area, which is 163.2 feet per lap:
5280 / 163.2 32.4 laps
Therefore, Joe needs to walk approximately 32.4 laps to cover one mile around his grass area.
Implications of Border Layout
The layout of the border can significantly affect the number of laps Joe needs to walk. For instance, if the border is circular, Joe would need the least number of laps to walk a mile because a circle is the shortest distance to cover a given area. Conversely, a long and narrow border, such as a rectangle that is nearly 72 feet in length, would require more laps to walk the same distance. The efficiency of the border shape directly impacts the number of laps and, ultimately, the time and energy Joe spends on his daily walk.
Conclusion
Joe's stone-paved garden not only enhances the aesthetic appeal of his yard but also influences the number of laps he needs to walk every day. By understanding the layout and design of the border, Joe can optimize his daily walk route to ensure he meets his mileage goals efficiently. Whether you're designing your own garden or optimizing an existing one, consider the shape and layout of the border to make the most of your outdoor space.