All Solutions - Attaching a Shed - January 22-26, 1996
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Correct solutions were submitted by:
Atlantic City HS, Atlantic City, New Jersey Zack Subin, Grade 9 Bethel Park High School, Bethel Park, Pennsylvania Peter DeFilippo, Grade 11 Cheshire High School, Cheshire, Connecticut Jennifer Davis, Jim Phillips, Grade 10 College Park HS, Pleasant Hill, California Rebecca Pearson, Grade 9 Curtis Junior High, University Place, Washington Aaron Biek, Grade 9 Curtis High School, University Place, Washington Gregg Erickson, Grade 10 David Mindess Middle School, Ashland, Massachusetts Nick Eromin, Grade 7 Fairfield High School, Fairfield, Connecticut Megan Booth, Grade 10 Bilal Seyal, Smita Chawla, Kyle Halligan, Grade 9 Granada High School, Livermore California Ethan L.R. Castor, Grade 10 Hinckley/Finlayson HS, Hinckley, Minnesota Lonny Bostrom, Matt Cabak, Grade 10 Juneau Douglas High School, Juneau, Alaska Christina Capacci, Cody Bennett, Grade 9 Mount St. Joseph Academy, Flourtown, Pennsylvania Jill Sommer, Grade 10 Murray Junior High, Ridgecrest, California Cassie Gorish, Grade 8 Thomas S. Kuo, Grade 7 Randolph Jr./Sr. HS, Randolph, Massachusetts Brad Jacobs, Grade 10 River Oaks P.S., York, Ontario, Canada Hassan Shamji, Grade 6 Sevastopol High School?, Wisconsin Ian Schuster, Grade 9 Smoky Hill High School, Aurora, Colorado Brian McCloskey; Somsnit Vanprapa; Yunny Chen; Kary Wyell, Grade 10 Bryon Joel, Scott Bridger, and Mark Overton, Grade 9 Sycamore School? George Mohler-DiMarzio and Jay Wetzel, Grade 8 Waluga Junior High, Lake Oswego, Oregon Julie Oest, Grade 8 Brian Gordon Dartmouth '92, Connecticut Jhonjon Tan DLSU, the Philippines
From: Bryon Joel,Scott Bridger, Mark Overton Grade: 9 School: Smoky hill Answer: The shed would be 8 feet up the wall on the mud room because in 12 feet, it would rise 24 in. + 6 feet is 8 feet. For the 2nd part the roof would need to drop 54 in. to reach 8 feet. 54 divided by 2 (inches dropped every foot) = 27, so it would go out 27 feet. ***************************************************** For every foot you go over you go down 2 inches, and if you go over 12 feet from the mud room wall to the outer wall of the shed you will go down 24 inches (12 times the 2). Since you end up 6 feet up and came down 2 feet just do it backwards and put the 2 feet back on and you have 6 + 2 = 8 feet high. If you continued the mud roof line from 12'6" until it is 8 feet off the ground you go down a total of 4'6". Take 4 times 12 + 5 = 54 inches. If you go out a foot for every 2" you come down, divide your total inches you come down by how fast your coming down (54 divided by 2 = 27 feet). The shed would have to come out 27 feet before it was 8 feet high. Peter DeFilippo Bethel Park ***************************************************** From: Julie Oest Grade: 8th School: Waluga Junior High Answer: Part 1: For each foot of the 12' length of the shed, the height of the roof goes up 2". That means the roof will go up 24", which is 2'. Adding the two feet to the 6 foot hight of the shed you get eight feet. So you will need to attach the shed roof eight feet up from the ground level of the mud room. Part 2: 12'6" - 8' = 4'6", this means the roof will have to go down 4'6" from the side of the mud room. Since the roof goes down 2" every foot you divide 4'6" by 2" to get the amount of feet the shed roof will extend out into the yard. This calculation comes to 27, which means the shed roof will go out 27' into the yard. ***************************************************** From: Aaron Biek Grade: 9 School: Curtis Junior High Answer: The roof has to go out 12 feet into the yard since the pitch is 1 foot for every 6 feet it travels out in the yard. If you start at 8 feet on the roof then you will end up at 6 feet for the end wall. The roof goes 6 feet into the yard for every foot of pitch so the roof will go 27 feet into the yard because it has to travel 4'6" of pitch. ***************************************************** Name : Lonny Bostrom School : Hinckley/Finlayson Highschool The shed roof needs to be attached 8 feet up the mud room wall. This is how I figured it out; if the end roof of the shed is 6 feet and the shed goes out into the yard 12 feet, take the 6 feet and rise 2 inches every time you run 1 foot until the run adds up to 12 feet. the final answer to this part of the problem is 8 feet. For the second part of the problem if the roof line of the mud room is 12 foot 6 inches rise, or in this case drop 2 inches and run 1 inch each time. Stop dropping when you get to 8 inches and count how many times you've runned. The number you come up with will be 27, this equals the measure of the length of the shed. ***************************************************** From: Christina Capacci Grade: ninth grade School: Juneau Douglas High School-Phoenix Program Answer: You should probably reconsider your roof's slope because it is VERY shallow. Problem one The roof must connect from a six foot high, twelve foot out wall. The roof rises vertically 2 inches for every horizontal foot. 12 x 2 = 24 inches the roof gains entirely feet inches per foot of horizontal gain The roof climbs 2 feet over its original height and thus intersects the mud room wall at eight feet. Problem two 12 1/2 - 8 = 4 1/2 existing feet, the feet of vertical feet of roof desired height difference above ground end point above ground 4 1/2 / 2 = 27 feet horizontally feet of inches, needed to be eight feet above vertical the amount of the ground difference vertical growth per one foot of horizontal gain It's good to think of this problem on an x and y axis graph. ***************************************************** From: Gregg Erickson Grade: 10 School: Curtis High School Answer: A: 8 feet up the mud wall, The answer was achieved by taking 12 and times it by 2-for the pitch then taking 24 and dividing by 12 - for inches to the feet the answer is 2 feet plus the original 6 which gives you a grand total of 8 feet. B: 27 feet out into the yard, You take 12'6" and subtract 8" for the intended height, then you take 4"6' and change it into inches you get 54 inches, then you divide by 2 for the pitch and you get 27 feet. ***************************************************** From: Brad Jacobs Grade: Sophomore (10) School: Randolph Jr./Sr. High School Answer: The answer to the first question is 8 feet because for each foot the roof rises 2 inches. Since there are 12 feet in all and the roof rises 2 inches for each foot the roof rises a total of 24 inches, which can be converted to 2 feet. Adding the 2 feet to the 6 foot wall we started with, we get 8 feet up the mud room wall. The answer to the second question is 27 feet into the yard starting at the point where the mud room meets the shed going until it is 8 feet off the ground. ***************************************************** From: Cody Bennett Grade: 9th School: Phoenix (JDHS) The shed would be attached at a height of 8'. The roof rises 2" for each foot it runs. The length of the shed will be 12', so the roof will rise 24"(12*2) which is 2'. The far wall of the shed is 6' high, so it will be attached to the mud room at 8' off the ground. If the roof of the mud room was continued, the shed would be 27' long before it is 8' off the ground. The difference of the height of the mud room roof (12'6") and the height of the end wall of the shed (8') is 4'6" or 54". Since the pitch is 2", the length of the shed will be 54" divided by 2" or 27'. ***************************************************** From: Nick Eromin Grade: 7 School: David Mindess Middle School, Ashland, MA Part I: To start off I knew the roof had a two inch pitch. Since it runs twelve feet out, I multiplied twelve and the two inches. I got twenty-four inches or two feet. I then added the two feet the roof rises to the six feet high the shed was and got eight. Therefor my answer is eight feet up from the ground is where the roof will hit the mud room floor. Part II: I knew the roof had a two foot pitch, so I multiplied two inches for the pitch and twenty-four feet out into the yard and got forty-eight inches (four feet). So I subtracted four feet from twelve feet six inches. I had six more inches to go. I did six inches left to go divided by the two inch pitch and got three feet. I added three feet and twenty-four feet and got twenty-seven feet. My answer is that it went twenty-seven feet out. ***************************************************** From: George Mohler-DiMarzio and Jay Wetzel Grade: 8 School: Sycamore School Answer: We figured out that the answer to the first part was 8' by multiplying the bottom 12' by the 2" pitch and then we added the 6' at the end. Next we subtracted 8' from the 12'6" and got 4'6" (54".) After that we divided 54 by 2 (because the pitch is 2" per foot) and got 27 feet as the answer to the bottom part. ***************************************************** From: Cassie Gorish Grade: 8 School: Murray Junior High Answer: #1. It has to be 8 ft. up the wall. I calculated that if for every foot 2 in. goes down, then in 12 ft. 24 in. goes down, or 2 ft. 6 + 2 = 8 (of course!) #2. 12'6" - 8' = 4'6" _2_ft._ + _2_ft._ + _6_in._ = 4'6" 12 ft 12 ft. 3 ft 12 + 12 + 3 = 27 ft. It would go 27 ft. into the yard. ***************************************************** Matt Cabak Sophmore at Hinckley Finlayson High School My solution is as follows: The shed wall is eight (8) feet tall My Explanation: If the pitch is 2 inches up to every foot horizontally, and the length is 12 ft, then the total difference is 24 inches (2 feet). 2 feet added to 6 feet is 8 feet on the mud room (sorry about the wordy solution) My Solution to the bottom portion is... 27 feet (not sure if correct) My Explanation: The roof line of the mud room is 12 feet 6 inches (150 inches) Shooting for 96 inches (8 feet) from 150 inches (12'6"), is a difference of 54 inches down. For every foot horizontally, you fall 2 inches, you divide 54 by 2 and get 27 feet! Thank You Matt Cabak ***************************************************** From: Ethan L.R. Castor School: Granada High School, Livermore Ca Answer: You must attach the the mud room wall at 8' The shed's roof would by 8' at the mud room wall. I got this by adding 2" to the 6' end wall and subtracting 1' from the distance from the mud room wall. My work is as follows 6' 6'2" 6'4" 6'6" 6'8" 6'10" 7'0" 7'2" 7'4" 7'6" 7'8" 7'10" 8'0" 12 11 10 9 8 7 6 5 4 3 2 1 0 For the second part, the roof would be 8' 27 feet from the mudroom wall. - Ethan ***************************************************** Name:Brian MCCloskey School:SHHS Grade:10 Before I started, I looked at all my givens. The roof was 6' tall and 12' long, the roof raised 2" for every 1 foot, and I had to find the difference in height between the house and the yard sides of the shed. Therefore I came up with the ratio of 12:2, for the raise of the roof. Since the length of the shed is 12', the raise of the roof would be 2'. I got this by thinking that if for every 12", the roof raised 2", then for every 12', the roof would raise 2', for every 120', the roof would raise 12', and so on. I basically just multiply each number by 10. Getting back to the problem, if the roof raised 2', it would meet up with the house at 8'. To check my answer, I told myself that the roof was 8' high next to the mud room, 6' high in the yard, therefore, what would be the length of that stretch of roof, with the ratio of 12:2. I then subtracted 6 from 8 and came up with 2'. This is the raise in the roof. If for every foot, the roof raised 2", then at how many feet would the roof raise 24"? I then divided 24" by 12" to get my answer. I came up with 12'. Since that was one of my givens, I knew that my answer is correct. Now for the second problem. The first thing I did here was list my givens; roof was 12'6" at the house, wanted to get where the roof was 8', and had the same ratio of 12:2. I then subtracted 8' from 12'6" to find out the distance of descent I would be accounting for. I came up with 4'6". I then converted 4'6" into inches, because the ratio of the slope of the roof is in inches, and I wanted to make everything have the same unit of measurement. I came up with 54". I then divided 54" by 2" and came up with 27'. This worked out the way it did because the roof had descended 54" and if the slope of the roof is 2" to every foot, then to get the number of feet, I had to divide the amount of descent by the number of inches per foot, since that was the given for the slope of the roof. My answer is that at 27' into the yard, the roof will be 8' off of the ground. Thank you for your time, Brian ***************************************************** From: Hassan Shamji Grade: Grade 6 School: River Oaks P.S. PROBLEM 1: The strategy I used was to create an algorithm. My equation was: 12 feet (floor length)* 2 inch pitch = 24 inches, which is 2 feet. That means the pitch makes the roof rise 2 feet and add that onto the base height of 6 feet comes to a total of 8 feet which shows that the shed roofing meets the mud room wall at 8 feet. PROBLEM 2: I also used the strategy of creating an algorithm. My equation was the following:Mud room roof height is 12 feet 6 inches and the roof has a 2 inch pitch and needs to get down to 8 feet. The roof has to go down 54 inches and with the 2 inch pitch it will stretch out 27 metres into the yard. ***************************************************** From: Somsnit Vanprapa; Yunny Chen; Kary Wyell Grade: 10 School: Smoky Hill High School Answer: The first question you asked is how far up the mud room wall the shed roof will need to be attached. To answer that question, I have tried to draw many diagrams. However, the diagrams seemed to mess up everything at once.I then found a better solution to this; it is, however, not about drawing so many diagrams at all. From the information given, The shed runs 12 feet out into the yard and is 6 feet tall. The slope is the same as the roof of the mud room, which is 2" for each foot it runs. To make this easier to calculate, I converted everything into inches. Then from the end wall of the mud room to the end of the shed (in the yard) is 144" (12'= 144").(12" is 1'.) The length of the end wall of the shed up from the ground is 72" (6'= 72".) I also have to keep the ratio in mind that it is 12":2".Now let's make a pattern out of this. Here are my data: 144 h ( stands for horizontal) 72 v (stands for vertical). From the point of 144 we have to go backward to the left a foot or 12" at a time. That means it will go up 2" each time too. So the next stops would be: 132h and 74v, 120h and 76v, 108h and 78v, 96h and 80v, 84h and 82v, 72h and 84v, 60h and 86v, 48h and 88v, 36h and 90v, 24h and 92v, 12h and 94v, 0h and 96v. That means when the pitches reach the mud room wall, it will be 96 " tall which is 8'. * The answer to the first question is 8' tall. The second question you asked is how far out into the yard the roof of the shed that continued from the roof of the mud room would be before it was 8' off the ground. The explanation to this question is very long, but since you did not ask for the explanation, then I shall just give you the answer with little explanation to it. We will have to work in the opposite way that we did with the first question. We know that it will start from 0" back into the yard, and the roof line of the mud room is 12'6" tall so it is 150" tall in another word. We shall subtract 2" from the height each time while we add 12" to the horizontal way. It will be 324" far out into the yard when it is 8' off the ground. In other word, it is 27' out into the yard. ***************************************************** Jill Sommer Grade 10 Mt. St. Joseph Academy Since for every foot, the roof goes up 2 inches, the roof would have to rise 24 inches to compensate for the 12 feet length of the shed. I added that to the 6 feet and decided that the shed roof would have to begin 8 feet up the mudroom wall. If the roof needed to be continuous from that of the mudroom and end up 8 feet off the ground, it would need to extend 27 feet from the end of the mudroom roof. To get this answer, I converted 12'6" and 8' to inches and got 150' and 96'. Then I subtracted 96 from 150 and got 54. Since for every 2 inches the roof went down, it went across 1 foot, I divided 54 by 2 and got 27. So, the roof would have to extend 27 feet from the mudroom in order for it to run continuously until it was 8' high off the ground. ***************************************************** From: Zack Subin Grade: 9 School: Atlantic City High School Answer: The height of the wall of the shed closest to the house would be eight feet. If the shed roof was built as an extension to the mud room roof, the shed's closest wall would have to be 27 feet away from the mud room wall. ***************************************************** Bilal Seyal, Fairfield HS, grade 9 I solved this problem by graphing. The wall between the mud room and the shed would be the y-axis and the ground would be the x-axis. I scaled the units to one foot apart. I go to the point (12, 6) which is where the roof ends on the shed. Since there is a two inch pitch, the slope is 2/12 or 1/6. But the line has a negative slope so it is -1/6. By graphing that line, the y- intercept is (0,8). So the shed roof will have to be attached 8 feet up the mud room wall. Since the mud room is 12'6" off the ground, the top would be the point (0, 12.5). The slope is -1/6 so the equation of the line is y = -1/6 s + 12.5, which is the roof of the mud room. If this roof was extended so that it was also the roof of the shed and if the end of the roof is 8 feet off the ground, then, by graphing, the shed would have to go out 27 feet into the yard. ***************************************************** Megan Booth, Fairfield HS, grade 10 1. If you want the slope of the shed of your roof to have a 2 inch pitch, the roof will rise 2 feet, making the mud room wall 8 feet tall. Since 12' = 144", 12"/2" = 144"/x; x = 2'. Add this to 6'. If the roof were flat, the shed would be a rectangle, and the mud room wall would be 6 feet tall. When you include the pitch, the wall is 8 feet. 2. By using a proportion, since pitch is proportional, 2"/12" = 54" (the roof line - end wall)/x (the length). x = 324" or 27'. P.S. Why not change the pitch of the roof on your shed so it won't leak on your motorcycle when it rains? ***************************************************** Smita Chawla, Fairfield HS, grade 9 1. The shed roof will need to be attached 8 feet high. If the pitch is 2 inches and the length of the shed is 12 feet, then 12 X 2 = 24" or 2'. This is because for every foot, you add 2" for the pitch. This is added to the 6' that we already had for the height so the shed roof will need to be 8 feet high. 2. The roof of the shed would go 27' into the yard. If you start at the top of the roof which is 12'6" and you have to go down to 8', then that is 4'6" or 54". Then 54" is divided by 2" to get the distance of how far the roof is into the yard. This is because if you have to go down 54" and the pitch is 2" then you just divide 54 by 2 and you get the distance of how far the roof is into the yard which is 27'. ***************************************************** Kyle Halligan, Fairfield HS, grade 9 1. The roof will attach at 8' up. This is because it goes up 2" every foot. So multiply 2 times 12 for this added height. That equals 24" which changes into 2'. You add that to the 6' already and you get 8' high. 2. The mud roof starts off as 12'6". This changes into 150". You'd like it to stop at 8' so that's 96". You subtract the two and get a difference of 54". You divide that by 2 and get 27' which stands for how far out the shed goes which is 27'. ***************************************************** From: Thomas S. Kuo School: Murray Junior High School, Ridgecrest, California Grade: 7th POW January 22-26, 1996 1. Answer to the first question is 8 feet. I got this by multipling 12 by 2. The answer was 24" or 2' and then I added it to 6'. The sum was 8 feet. 2. Answer to the second question is 27 feet. First I subtracted 12'6" by 8' which was 4'6". I converted 4'6" into inches which was 54". Then I divided it by 2" and got 27'. ***************************************************** From: Ian Schuster Grade: 9 School: sevastopol Answer: For the first answer the height of the shed is 8'. All I did to get this answer was to divide twelve (distance) by two (the slope of the roof) and added it to 6' feet (the other side of the shed). For the second answer I got 27'. to get this answer I subtracted 8' (the height of the shed) from 12.5" (the height of the mud room) which is 4.5' (the distance the roof hadto go, to get to be 8' off the ground. Then I divided my answer by 2 (the slope of the roof). ***************************************************** Jennifer Davis Grade 10 Cheshire High School Cheshire, ct The shed is 12 feet long and at the end 6 feet high. It rises 2" every foot going back towards the mud room. If the shed is 12 feet long and rises 2" for every foot then the shed will rise (12'*2") = 24" which also equals 2 feet. Since the wall began at 6 feet and it inclined 2 fet the height of the shed when it reaches the mud room is 8 feet. The roofline of the mudroom is 12'6" off the ground. If the roof of the mudroom continued down to the roof of the shed it would end at 8 feet. 12'6" - 8' = 4'6". So if the roof declines 2" for every foot and it needs to decline 4'6" we will have to divide the length needed by 2" to get how far out the shed will extend. Since 4'6" also equals (4 * 12 ) = 48" + 6 =54". (54"/2") = 27" . ***************************************************** Jim Phillips Grade 10 Cheshire High School Cheshire CT. 06410 1. The shed wall attached to the mud room will need to be 8 feet tall. The roof pitch is 2 inches per 1 foot. You have 2 * 12 feet which is equal to 24 inches which the turns int 2 feet plus the original six feet gives you an eight foot wall. 2. Starting with a height of 12 feet 6 inches and you want to get to 8 feet thats 54 inches you need to lose in height. 12 inches per foot, 4 feet equals 48 inches plus the remaining six gives you 54 inches which turns into 27 feet. The shed will jet out into the yard 27 feet. ***************************************************** Rebecca Pearson, ninth grade College Park High School, Pleasant Hill If the roof rises 2" for every foot long it is, and the roof is 12 ft. long, then it will rise a total of 24", or 2 ft. above its beginning height ( the outside wall) of 6 ft. SO you will need to attach the root 8 ft. from the ground on the mud room wall. To get the mudroom roof that has a pitch of 2" and a height of 12' 6" to go down so its ending height would be 8', you take the vertical distance between 12' 6" and 8' (the ending height of the shed) and divide it by 2". So 4' 6" divided by 2" = 27. This is the number of feet it would extend into the yard. (27' x 2" = 4'6") ***************************************************** From: Brian Gordon School: Dartmouth '92 For the first part: Since the roof's height gains two inches per every foot, it will gain twenty-four inches, or two feet, over the twelve-foot length of the shed. So the roof should start two feet higher than its lower end, or six = two = eight feet high. For the second part: You want the roof to drop four feet, six inches. This is equal to twenty-seven intervals of two inches. Since the roof falls two inches for every foot of length, the shed must be twenty-seven feet long just to get it down to eight feet high. That's quite a shed! --Brian ***************************************************** From: Jhonjon Tan Grade: School: dlsu Answer: ====== X = ============ = ========= 6 =============== = = =============== 12 from the figure we get x=(12')*(1/6)=2 feet therefore the height is 6 2=8 feet. For the second problem, let the unknown be x x=(4'6'')(1/6)=27 feet.
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