All Solutions - Earthquake! - May 6-10, 1996
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Correct solutions were submitted by:
Akiba Hebrew Academy, Merion, Pennsylvania David Love, Grade 11 The Brandon Hall School, Dunwoody, Georgia Dong Woo Jee, Grade 9 Cheshire High School, Cheshire, Connecticut Paul Laconte, Rosina Pannone, Anonymous, Caryl Anquillare, Don Kim, Grade 10 College Park HS, Pleasant Hill, California Rebecca Pearson, Angie Bush, Philip Horner, Jacqulyne Law, Grade 9 Cygnet, Tasmania, Australia Amy Forster, Age 11, homeschooled Franklin County High School, Rocky Mount, Virginia Rita Beckner, Mark Winesett and Kelli Preston, Grade 9 Fremantle Senior High School, Fremantle, Western Australia Connor Stokes and Sean McKaay, Year 9, Cameron Davis, David Saw, Year 8 Georgetown Day School, Washington, DC Leah Rinaldi, Josh Hersh, Phoebe Stone, Grade 8 Granada High School, Livermore, California Ethan Castor, Simon Kerbel, Grade 10 Iolani School, Honolulu, Hasaii Jason Yeung, Grade 9 J. P.Taravella High School, Florida Brent Tworetzky, Grade 9 Martin County High School, Stuart, Florida Seth Rients, Rod Hofer, Grade 9 Mercer Island High School, Mercer Island, Washington Connie Hanson and Cara Hanelin, June Yoo, Jordan Hom, Grade 9 Mount Saint Joseph Academy, Flourtown, Pennsylvania Shannon Firth and Joanne Getson, Liz Croney and Annie McIntyre, Carolyn DiMaria, Grade 9 Murray Junior High, Ridgecrest. California Ryan Carpenter, Cassie Gorish, Grade 8 Thomas Kuyo, Grade 7 North Cross School, Roanoke, Virginia Glen Mackey, Grade 9 Riverside Jr./Sr. HS, Taylor, Pennsylvania Sean McGinnis, Grade 12 South Secondary School, London, Ontario, Canada Luke Neville, Grade 10 St.Johns, Montreal, Quebec, Canada Keith Cusson, Grade 7 Walnut Hill, Natick, Massachusetts Will Donnelly, Grade 11 Rachel Schneebaum & Ashima Scripp, Grade 10 Ali Monchick, Grade 9 Waluga Junior High, Lake Oswego, Oregon Branden Tarlow, Grade 7 Brian Gordon, Dartmouth '92, Middletown, Connecticut
From: Ryan Carpenter Grade: 8th School: Murray Junior High Answer: I used the Pythagorean Theorem to solve the problem: .7^2 + 5^2 = x^2 .49 + 25 = x^2 25.49 = x^2 5.05 = x (approximate) Steve lives .7 mile from the epicenter. Steve lives approximately 5.05 miles from the actual spot of the earthquake. ************************************************ From: Jason Yeung Grade: 9 School: Iolani School Answer: The epicenter is .7 miles from Steve's house. The distance between the actual spot is the square root of 2549 and all over 10 [after being asked for an explanation...] The actual spot, epicenter, and Steve's house form a right triangle like this. Steve's house .7 miles epicenter __________________ \ |_| \ | \ | \ | \ | \ | \ | \ | 5 miles underground \ | \ | the distance we are finding \ | \ | \ | \ | \ | \ | \ | \| actual spot Therefore, to solve the second part of this question, I can use the Pythagorean Theorem. 2 2 2 a + b = c so the answer is .7 square plus 5 square is c square. 2 25.49 is c so the answer is the square root of 25.49 miles, or approximately 5.0489976 miles. For the first part, I just subtracted 6.3 miles from 7 miles and got .7 miles because they are on the same direction. Jason ************************************************ From: Brent Tworetzky Grade: 9 School: J.P.Taravella (in S Fla.) This question has two parts; if I understand it correctly, seeing as Steve's house and the epicenter are along the same line, Steve's house is (7-6.3) or .7 miles from the epicenter. Then, using a right triangle with sides .7 (along the ground, epicenter to Steve's house) and 5 (vertically down from the epicenter), we get 5 squared, or 25, and .7 squared, which is .49. 25 + 49 = 25.49. The square root of 25.49, the distance from Steve's house to the earthquake, is approximately 5.048762224546. For further explanation if necessary; A 2 2 2 .49 **** BY PYTHAG THEOREM, A + B = C. THEN, **** * * 2 2 2 * * B ** C .7 + 5 = X 5 ** * .49 + 25 = 25.49 * The square of root of 25.49 is about 5.048762224546. ************************************************ Steve's house is 5.048 miles from the actual underground spot of the earthquake, and .7 miles from the epicenter. Steve's house is .7 miles from the epicenter because his house is 7 miles ENE of Duval, and the epicenter was 6.3 ENE of Duval. Ethan Castor Granada High School Livermore, Ca 10th Grade ************************************************ Answer: 1. Steve's house is 0.7 miles from the epicentre. 2. Steve's house is 5.05 miles away from the actual spot of the earthquake Solution: 1. Steve's house is 7 miles - 6.3 miles = 0.7 miles from the epicentre. 2. I formed a triangle with a right angle at the epicenter; and joined the epicenter, Steve's place, and the actual center of the earthquake, as vertices. Using Pythagoras' Theorem, distance of Steve's house from actual center ^2 = distance from Steve's to epicentre^2 + distance of epicentre to actual centre^2 = 0.7^2 + 5 ^2 = 25.49^2 So distance of Steve's house from actual center = sqrt25.49 = 5.05 miles I am interested in finding out what the magnitude of the quake was by the time it got to Steve' house. I think I will need to know what force a 5.4 magnitude quake has. I think it must be terrifying to live in your part of the world where there are so many earthquakes. I hope Steve has a peaceful summer! From Amy Forster, age 11, grade 7, Cygnet, Tasmania, Australia. Wilkins/Forster family Crooked Tree Point. Cygnet. Tasmania. Australia ************************************************ From: Cassie Gorish Grade: 8 School: Murray Middle School Well, the first part was easy.r7 - 6.3 = .7 so he lives .7 miles away from the epicenter. The second part uses the Pythagorean Theorem. ____.7____H | / 5 | / | / | / | / X | / | / | / | / |/ E Point H is where Steve's house is. Point E is actually where the earthquake occurred. X is the distance from point E and point H. Here comes the Pythagorean Theorem: (Length of Leg 1)squared + (Length of Leg 2)squared = (Length of Hypotenuse)squared 5 squared + .7 squared = Hyp squared 25 + .49 = Hyp squared 25.49 = Hyp squared Approximately 5.049 = Hypotenuse So his house is approximately 5.049 miles away from the place where the earthquake actually occurred. ************************************************ I believe he was .7 miles from the epicenter and roughly 5.05 miles from the actual spot. Let me have more info on the second part with the magnitude. Sean McGinnis | 12th grade | Riverside Jr./Sr. High School Taylor, Pa 18517. ************************************************ From: Keith Cusson Grade: 7 (8 math) School: St. John's The answer is 5.048762225 miles away. The way I figured it out is I thought of the area it hit as a sphere. The epicentre 5 miles down is the centre of the sphere. Then I used the Pythagorean Theorem to figure out the distance. That is how I got my answer. ************************************************ From: Branden Tarlow Grade: 7, 8 School: Waluga Junior High, Lake Oswego, Oregon Answer: Steve's house and the epicenter fall on the same ENE line from Duval. By finding the distance I determined Steve's house was .7 miles away from the epicenter. A right triangle with sides 5 miles and .7 miles is formed. Using the Pythagorean Theorem it can be determined that Steve's house was approximately 5.049 miles from the actual earthquake five miles underground. ************************************************ Connie Hanson, Cara Hanelin Algebra; 9th grade Mercer Island High School There is .7 miles from Steve's house to the epicenter, and the earthquake occurred 5 miles below the earth. We made a sketch showing this. We wanted to figure out the other side of the triangle, and that would give us the length from Steve's house to the earthquake. We used the term "sohcahtoa" to figure out our chosen angle. Because it is the length of the hypotenuse you don't know, we used the formula tan x=opp. / adj. We substituted .7 for the opp. and 5 for the adjacent. It gave us .14, but we needed to find the angle, so we did tan -1 and it gave us 7.97°. We then chose sin x=opp. / adj., we substituted x for the hypotenuse. Our formula then looked like sin 7.97=.7/x. We cross-multiplied and found that x, the length of the hypotenuse, is 5.049 miles, the distance from Steve's house to where the earthquake occurred. ************************************************ From: Thomas Kuo Grade: 7 School: Murray Junior High School 1. Steve's house is 0.7 miles from the epicenter of the earthquake. I got this by subtracting Steve's distance from Duval by the epicenter's distance from Duval. 7-6.3 = 0.7 2. Steve's house is sqrt 25.49 miles from the actual spot of the earthquake (about 5.05 miles). I got this by using the Pythagorean Theorem. I substituted a = 0.7 and b = 5. ************************************************ Point A is the epicenter. Point B is Steve's house. Point C is the actual place of the earthquake. Since Triangle ABC is right, AB squared plus AC squared equals BC squared. Therefore, .7 squared plus 5 squared equals 25.49. BC equals 5.05. Steve's house is .7 miles from the epicenter. The distance from Steve's house to the actual spot of the earthquake is 5.05 miles. Rita Beckner grade 9 Franklin County High School Rocky Mount, Virginia ************************************************ From: Luke Neville Grade: 10 School: South ss, London, Ontario Answer: The epicenter was .7 miles away from Steve's house. The earthquake itself was 5.0 miles away (the square root of 25.49, rounded to one decimal place accuracy) Luke ************************************************ From: Seth Rients Grade: 9th School: Martin County High School His house is .7 miles from the epicenter, and his house is the square root of 25.49 from the exact spot of the earthquake. ************************************************ June Yoo Geometry 9th Grade Mercer Island High School The epicenter was 6.3 miles ENE of Duval and Steve' s house was 7 miles ENE of Duval. So 7-6.3=.7. Then Steve's house would be .7 miles from the epicenter. The actual earthquake was 5 miles deep. This creates the right triangle in the drawing. If you use the Pythagorean Theorem: 5 squared + .7 squared must equal the distance of Steve's house to the earthquake squared. 5 squared + .7 squared = 25.49. So the square root of this would be the actual distance. The square root of 25.49 = 5.048.... ************************************************ Jordan Hom Geometry, 9th grade Mercer Island High School I created a sketch of what the situation would look like in 2-D. Next, I simply used the Distance tool in the Measure menu to determine the distance from Steve's to the Epicenter, and from Steve's to the Origin of the earthquake. Distance of Steve's to Epicenter = .7 miles Distance of Steve's to Origin of Earthquake approximately 5.1 miles ************************************************ David Love 11th grade Akiba Hebrew Academy Since Steve's house is 7 miles away from a set location, and the earthquake (or epicenter) was 6.3 miles away, then Steve's house is .7 miles away. To figure out how far away from the actual spot it is, you can form a right triangle where the distance between the two (.7 miles) squared, plus how far the earthquake was underground (5 miles) squared, equals the square root of the distance from Steve's house to the actual spot of the earthquake. Therefore, 25 + .49 = 25.49, which square rooted is 5.048, or the distance in miles between the house and the quake. ************************************************ From: Simon Kerbel Grade: 10 School: Granada High School Steve's house is 0.7 miles from the epicenter, and he is 5.049 miles from where the actual earthquake took place. I used the Pythagorean Theorem to solve this problem. ************************************************ From: Will Donnelly Grade: 11 School: Walnut Hill, Natick MA Answer: Steve's house is exactly 0.7 miles from the epicenter and he was approximately 5.049 (exactly sq root of 25.49) miles from the exact spot of the earthquake. ************************************************ From: Ali Monchick Grade: 9 School: Walnut Hill, Natick MA Steve's house is 0.7 miles from the epicenter. It is approximately 5.048 miles from the earthquake (by the Pythagorean Theorem). ************************************************ From: Rachel Schneebaum & Ashima Scripp Grade: 10 School: Walnut Hill, Natick MA Steve's house is 0.7 miles from the epicenter and 5.05 miles approximately from the actual spot of the earthquake. ************************************************ From: Glen Mackey Grade: 9th School: North Cross School, Roanoke, Virginia The epicenter of the earthquake and Steve's house are both ENE of Duval. This means that if a straight line was drawn ENE of Duval it would pass through the epicenter and Steve's house. Now it becomes a simple subtraction problem. The distances are subtracted, 7 miles - 6.3 miles, leaving 0.7 miles between the epicenter and Steve's. To figure out how far it is from the actual spot of the earthquake and Steve's is a simple Pythagorean Theorem problem. The fact that actual spot of the earthquake is 5 miles directly below the epicenter forms one of the legs. The distance from the epicenter to Steve's house forms the other leg, 0.7 miles. The distance from Steve's to the actual spot of the earthquake is the hypotenuse. First you square 5 and 0.7, and add their products. This gives you 25.49. Then you take the square root, giving you the distance as being about 5.04 between the actual spot of the earthquake and Steve's. ************************************************ Connor Stokes and Sean McKaay Year 9 13 y.o. First we must redefine the question. How far is Steve's house from the epicenter and how far is his house from the actual earthquake to a sensible accuracy. To start we look at the information given to us. Steve lives near Duval, Washington. This is about 30 miles north and east of Seattle where the person doing this article is living. The above information is quite useless when it comes to the actual question but it does set the scene and it tells us where Duval is. Steve lives 7 miles ENE of Duval, the epicenter was 6.3 miles ENE of Duval and the actual earthquake was 5 miles underground. This is quite important because saying that Steve lives 7 miles out of Duval and the epicenter was 6.3 miles out of Duval does not mean that they are on the same bearing. However they are on the same bearing (ENE) and as such it is quite simple to work out how far from the epicenter Steve's house is. We take 6.3 from 7 and we get 0.7 miles. With this information we can start to construct a model (See Diagram.)This model is a right angle triangle, we know what a and b equal but now we must work out what the hypotenuse or h equals. To do this we will use Pythagoras's rule. This rule is that h2 = a2 + b2 or h equals the square root of a2 +b2. So a2 is 25 and b2 is 0.49. We add these together and we get 25.49 so we can update our equation of h2 = a2+b2, we now have h2 = 25.49. So we must find the square root of 25.49. This is a simple process in this day in age, just take out the old calculator, punch in a couple of numbers and we have the answer of 5.0486762225. We could just give this as the answer and be done with it however this is much too accurate for the example. In the problem the numbers are given quite roughly and the most accurate it gets is to 1 decimal place (the epicenter was 6.3 miles from Duval). To show this we will break down the answer, the answer was 5.0486762225. This is 5 miles, 48 metres, 67 centimetres, 2 millimetres and 225 micro metres. This is ridiculous, so we get rid of the micrometres to start with. This is still ridiculous, so we have to get the number to 1 decimal place, so it coincides with the most accurate number used in the problem. If we do this we get 5.0 miles, this is not accurate enough however because the side must be more than 5 miles because side a is 5 miles long. So we go to 2 decimal places and we get 5.05 miles, this is more suitable and this is our answer as accurate as is possible. By Sean Mackaay and Conor Stokes South Fremantle Senior High School Western Australia ************************************************ Cameron Davis Year 8 13 y.o. Steven's house is 0.7 miles away from the epicentre and he is 5.O4 miles from the actual earthquake. To get the second answer times the two shorter sides of the right angle triangle by themselves and add them together. This then equals 25.49, find the square root of this and you have your answer, 5.O4. ************************************************ David Saw Year 8 13 y.o. It is .7 miles from Steve's place to the epicenter. To get the answer you will have to subtract 6.3 from 7. The answer to the problem "How far is it from Steve's to the Earthquake point" is 5.04 miles. To get this you will have to draw a line straight down that is 5cm long (1cm for every mile) and draw a line from Steve's to the Earthquake point. You will find it measures 5.04 cm. (5.04 miles to scale) David Saw. South Fremantle Senior High School. Year 8. Form 8S3. Age 13. E-Mail ************************************************ Paul Laconte Grade 10 Cheshire High School Cheshire CT Annie, since this is not a right triangle, the most common way to find the missing side is by using the Pythagorean Theorem. You know that this is not right triangle because the problem says so. So I plugged in the numbers in the correct places. I used the formula a^2= b^2 + c^2. I substituted .7 and 5 for b and c (7 miles minus 6.3 miles and five miles below the surface). So now my equation is a^2= .7^2 + 5^2. After using my TI-82 I discovered the next step in the equation. This is a^2 = .49 + 25. Now, to find a alone I have to find the square root of a as well as 25.49. Lastly, the square root of a^2 = the square root of 25.49 this number is 5.05. Thus the distance from his house to the actual earthquake is 5.05 miles. Thanks for another difficult problem! ************************************************ Rosina Pannone Grade 10 Cheshire High School Cheshire, CT Steve's house is 0.7 miles away from the epicenter and 5.05 miles away from where the earthquake actually occurred. To get how far away Steve was from the epicenter, I used the given in the problem. The problem stated that Steve's house is 7 miles ENE of Duval, and the epicenter is 6.3 miles ENE of Duval. So, it's a simple matter of subtraction to find out the distance from the epicenter to Steve's house. The distance is 0.7 miles. To find the distance from the earthquake to Steve's house, I used the Pythagorean Theorem. The problem says that the earthquake is 5 miles directly below the epicenter. This makes the line between the epicenter and the earthquake perpendicular to the line from the epicenter to Steve's house. I then made a line segment connecting the earthquake and Steve's house. This made a right triangle. Since the measurements of the legs were known, I used the Pythagorean Theorem to figure out the hypotenuse (the distance from the earthquake to Steve's house). The distance was 5.05 miles. ************************************************ ?? In figuring out this week's Problem of the Week, I found that the epicenter of the earthquake was .7 miles away from Steve's house. I came to this conclusion by subtracting the number of miles between Duval and the epicenter from the number of miles between Steve's house. Next, I found the distance between the beginning of the earthquake (.7 miles away and 5 miles down) and Steve's house. To do this, I made a right triangle with one side being .7 and the other being 5. I found the hypotenuse by using the formula; a^2+b^2=c^2. The distance between the house and the actual beginning of the earthquake turned out to be 5.05m. ************************************************ Caryl Anquillare Grade 10 Cheshire High School Cheshire, CT Steve's house is .7 miles from the epicenter and 5.05 miles from the actual spot of the earthquake. If it happened 6.3 miles ENE of Duval and he lives 7 miles ENE of Duval, then 7 - 6.3 = .7. So he lives .7 miles away from the epicenter. And because the epicenter is directly above the actual spot, it is perpendicular from the spot to the epicenter and from the epicenter to him. So the triangle would be one side .7 miles, the next angle would be 90 degrees, and the other side on the other side of the angle would be 5 miles. By Law of Cosines, the last side = 5.05 miles. ************************************************ Don Kim Grade 10 Cheshire High School Cheshire, CT. Steve's house is .7 miles from the epicenter. I got this by subtracting 6.3 from 7, this is because Steve's house is 7 miles away from Duval and epicenter is 6.3 miles, so to find the distance between you just subtract. To find the distance of his house from the actual spot of the earthquake, I had to use the Pythagorean theorem. Since it was 5 miles underground, it would from triangle if you connect the epicenter, Steve's house and the underground point. You needed to know the hypotenuse, so it's this (5^2+.7^2=h^2). I got the answer to be approximately 5.1 miles. So Steve's house was about 5.1 miles away from the actual spot of the earthquake. Thanks, Don Kim ************************************************ Steve lives .7 miles from the epicenter, and he is the square root of 25.49 or 5.048762225 miles from the quake itself. I used a triangle to solve the problem. I used the two sides you gave us (5 and .7) to find the hypotenuse, which is also the distance from the quake. Rod Hofer/MCHS/Limber ************************************************ Shannon Firth and Joanne Getson Grade 9 Mount Saint Joseph The problem this week was a lot of fun. It had a lot to do with triangular theorems which we knew a lot about. The map we made looked like this: We then used the Pythagorean Theorem to find the distance of how far the house was from the actual center of the earthquake. The actual distance was the square root of 25.49 miles, or about 5.04 miles. ************************************************ Liz Croney and Annie McIntyre Mount Saint Joseph Grade 9 After reading the problem the first thing we did was find the distance between Steve's house and the epicenter. 7 - 6.3 = .7 (miles). Next we were asked to find the distance between Steve's house and the actual earthquake. We did this by making a right triangle with the unknown distance as the hypotenuse. The legs were .7 miles and 5 miles. We then got 5.1 miles by using the pythagorean theorem. This was the distance between Steve's house and the actual earthquake. ************************************************
************************************************ Leah Rinaldi Georgetown Day School 8th grade Paul Nass
Steve's house is 7 ml ENE of Duval and the epicenter is 6.3 miles ENE of Duval. So Steve's house is .7 miles from the epicenter. His house was the square root of 25.49 miles from the earth quake. A squared + B squared = C squared .7 squared + 5 squared = C squared .49 + 25 = C squared The square root of 25.49 = C ************************************************ My name is Dong Woo Jee. I am in the ninth grade at The Brandon Hall School in Dunwoody Georgia. Currently I am taking geometry with Mr. Earley. Using the Pythagorean Theorem we can find the distance between Steve's house and the earthquake. C^2 = A^2 + B^2 X^2 = 25 + 0.49 X^2 = 25.49 X = 5.042816673 or square root of 25.49. ************************************************ Rebecca Pearson, College Park High School, Pleasant Hill, California Since the epicenter and Steve's home are on the same line from Duval, Steve is .7 miles away from the epicenter. To find how far he was from the actual earthquake, make a right triangle with his distance from the epicenter as one leg and the distance from the epicenter down to the actual earthquake as the other leg. Use the Pythagorean theorem to find the hypotenuse, which is the distance from Steve's home to the actual earthquake. The distance between Steve's home and the earthquake is 5.05 miles. ************************************************ Angie Bush Because the spot where the earthquake happened is directly below the epicenter it is perpendicular to the line the epicenter and Steve's house is on. This creates a right triangle with the hypotenuse being the distance from where the quake happened to Steve's house and the other two being the distance from the quake to the epicenter and from the epicenter to Steve's house. By using the Pythagorean theorem the distance can be found. Steve's house is 5.05 miles from the spot the earthquake hit. ************************************************ Philip Horner The first thing that I did in order to solve this problem was to draw out the problem and write down all the measurements. The next thing that you wanted to know was how far Steve's house was from the epicenter. If the epicenter was 6.3 miles from Duval, and Steve's house is 7 miles from Duval, then to find the distance from Steve's house to the epicenter I subtract 6.3 from 7. So Steve lives .7 miles from the epicenter. The next thing that you asked was how far Steve lived from where the actual earthquake took place. To find this out I used the Pythagorean Theorem. Steve's house to the epicenter is one leg, .7 miles and the epicenter to the earthquake is the other leg, 5 miles. So I fill in the variables a and b with .7 and 5 and figure the problem out. Steve lives about 5.049 miles away from the actual earthquake. ************************************************ Jacqulyne Law First I drew myself a picture or a map so that I can understand what you were talking about. You said that the epicenter is 6.3 miles east-north- east of Duval, and Steve's house is 7 miles east- north-east of Duval. So, it means that , that are in the direction so it is .7 miles from Steve's house to the epicenter, because it is 7 miles and 6.3 miles so is 7-6.3 miles =.7 mile. That solved the first part of the question. I was really glad that last week I had to read a chapter earthquake and it talks about the stuff that you mentioned in the POW. The actual place is called the force of the earthquake, and to find out the distance from force to Steve's house, I used the Pythagorean theorem. Since I knew the legs of the right triangle, one is .7 miles and the other is 5 miles. So it is about 5.05 miles from Steve's house to the force of the earthquake. ************************************************
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************************************************ From: Brian Gordon Grade: 1992 School: Dartmouth This seems like an easy one. How about .7 miles from the epicenter (since apparently the epicenter, Duval, and Steve's house are collinear) for Steve's house. And then the square root of 25.49 miles from the actual location of the quake. (Can you say Pythagorean?) :) Actually, these numbers wouldn't be perfect, because I'm applying plane geometry to the surface of a sphere. I don't have the distance formulas for computing between latitude/longitudes around here, but the nearness of the places, on a global scale, shouldn't affect the answers by too much! --bri
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