John is designing a redwood deck. each board is 5 1/2 inches wide, and each will be placed parallel to one another. Should he use 3/16 inch, 1/4 inch, or 3/8 inch spacing between boards if he wants the deck to be as close as possible to, but not greater than, 18 fet wide? How wide will the deck be?
These non-metric units always confuse me, so since I use metric most of the time, I will convert to decimals
consider 1 board + 1 gap to be one unit
so we have
6.5 + .1875 = 6.6875 inches
6.5 = .25 = 6.75
6.5 + .375 = 6.875
now... 18 feet = 216
216/6.6875 = 2.6932.299..
216/6.75 = 32
216/6.875 = 31.418..
Since the second of these comes out exactly
the gap should be 1/4 inch
(your actual question of "How wide will the deck be" makes no sense, since you told me it was 18 ft wide)
To determine the spacing between the boards and the resulting width of the deck, we need to consider the total number of boards and the additional spacing between them.
First, we need to calculate the number of boards required to achieve a width of 18 feet. Given that each board is 5 1/2 inches wide, we can convert the deck width to inches:
18 feet * 12 inches = 216 inches
To find the number of boards, we divide the deck width by the width of each board:
216 inches รท 5 1/2 inches = 39.27 (approximately)
Since we cannot have a fraction of a board, we need to round down to the nearest whole number. Therefore, John will need 39 boards for his deck.
Next, we need to decide on the spacing between the boards. We have three options: 3/16 inch, 1/4 inch, and 3/8 inch. The goal is to choose a spacing that is as close as possible to, but not greater than, the desired width.
Let's calculate the total spacing required for each option:
- For 3/16 inch spacing:
(39 boards - 1) * 3/16 inch = 7 3/16 inches
- For 1/4 inch spacing:
(39 boards - 1) * 1/4 inch = 9 3/4 inches
- For 3/8 inch spacing:
(39 boards - 1) * 3/8 inch = 14 5/8 inches
Finally, we add the total spacing to the total width of the boards to get the overall width of the deck:
- For 3/16 inch spacing:
216 inches + 7 3/16 inches = 223 3/16 inches
- For 1/4 inch spacing:
216 inches + 9 3/4 inches = 225 3/4 inches
- For 3/8 inch spacing:
216 inches + 14 5/8 inches = 230 5/8 inches
To determine which spacing to use, we need to choose the option that is closest to, but not greater than, 18 feet (216 inches). Therefore, John should use 3/16 inch spacing, and the width of the deck will be 223 3/16 inches or approximately 18 feet 7 3/16 inches.