Es322 Example Quantitative Problem Solving Techniques With Solutions
ES322 EXAMPLE QUANTITATIVE PROBLEM SOLVING TECHNIQUES WITH SOLUTIONSPrimer on Solving Quantitative Style Word Problems in Physical Science and GeologyStudy Technique: Follow the step-by-step problem solving method outlined below; review the attachedexample problems and solutions; practice repetitively and compare your answers to key.(1) Carefully read the word problem(2) Identify all the variablesa. ID Knownsb. ID Unknowns(3) Draw and sketch the problem, labeling all the variables with magnitudes and units(4) Convert all units to consistent dimensions; use unit algebra techniques, cancel units(5) List all equations that apply to the problem, refer to class notes and text book(6) Rearrange equations, substitute variables, algebraically solve for the unknown(s)(7) Check your work, review your math, review your unit algebra, does the value of your answermake logical sense? For example, if you calculate the volume of the Earth as 6 gallons,something is not right, and you need to go back to the drawing board.Example Problem 1.2 Assume you are dealing with a vertical‐walled reservoir having a surface area of500,000 m2 and that an inflow of 1.0 m3/sec occurs. How many hours will it take to raise the reservoirlevel by 30 cm?Stepwise solution to problem 1.2
G476/576 HydrologyIntroduction to Applied Problems in HydrologyDetennine the following, show all of your math work and unit algebra.(j) A city has a reservoir with vertical sides and a surface area of 12.3 acres.Following the rainyseason, the reservoir is filled to a depth of3.0 m. During the dry season, the reservoir loses 3.5 inofwater per week (wk) to evaporation. At the same time, the city pumps water from thereservoir at a rate oflOO gaVday. What volume of water will remain in storage after 3 weeks intothe dry season? (answer in cubic meters, and gallons)(DHow long must a pump with a capacity of25 gaVrnin pump to fill a tank with a capacity of60cubic meters?.Q)A small urban watershed has an area of20.5 square miles. A summer stonn drops an averageof2.5 in ofrain over the entire watershed. If65% ofthe rainfall runs off the watershed intosurface-water bodies, what is the volume ofrunoff(show all of your work and unit algebra):A. In cubic inches?B. In cubic feet?c. In cubic meters?
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1,,( ath{,l-( () re ko i /0"" 113 INTRODUCTION TO TOPOGRAPHIC MAPSc:lwou\geomorphV2000Vntrolab. wpdAll of the following questions refer to the Monmouth, OR Quadrangle.1) What is the fractional scale, contour interval, and magnetic declination of this map?a) Scale: I : ;)'1,OO(Jb) Contour Interval: W L,c) Declination: Iqc{2) What quadrangle maps are located immediately adjacent to the Monmouth Quad.?c) East: S;d LId) West: Alelie Noetha) North: ic.'K-re \ b) South: I.J vV\'3W 3) What is the quadrangle size series of this map (in long. and lat.)?f,5 mi()4) What is the date of publication of this map?1t11O ( hoto ('ev\-;)ed 11'6125) What does the tick with 4956000m N. mean? (lower right of map)1jTtJ\ demOJU\tIO'(\6) What is the name of the major fluvial system flowing through this area. Of What larger drainageabasin(s) does this river form a part of?0)1! \ictrne fe q \vey--ICoILJr l'f::J I 0.'KIV-e,PC\S IV]7) What is the approximate elevation of the Natural Sciences Building based on the maprepresentation? 3-10-f 8) Given the fractional scale determine the following {I()c21f,O{)O,i\5 inches on the map 10 inches on the map 9)10)10Feet on ground \. ?/IMeters on ground (,.0:1 LeCJtJ t-. & Miles on ground.Kilometers on ground. 2"'t 1k 'CY,IDODM':.l14mA. What is the road distance in miles along Rt. 99 between Helmick State Park and Monmouthcity limits? \O In x 2LtDX7 31l,OCO '''Cf;y) S2% 4)'' ! .g;1 r'llJlt"SB. What is t e distan j k ters:Y.::ffi \: f.Q3 -rY\LtP\d \Y\\ ":7. -l."l :-S 1:\OOOm JA. Determine the average stream gradients (in FtlMi) for the following drainages:X A. Willamette River:B. Luckiamute River:11 )SJ.iiOf - IVV'I'\\ 'd-\0 {f -"Gradient: \:t-1--\ 3 "- 24- dLength: 105- 2,\'Yl1 1J.,y\\Gradient).ll- IS't ,: 5!:JNLength: n-s 1 11 A. What is the highest point of elevation represented on this map?,1,?)\ -1-I Oft?)rY\;,. .ft- i-30 .}1 What is the longitude and latitude location of Davidson Hill?\: By.4-"4:')'C;A" 1;)."2,1\1\) 1:5/1C. What is the straight line di t ce in mile betw n these two pOints?5 If) x 2Lt, 0)0 I'1D,CCO I ,,( 2. \ .,"') ·0:1. (;L0d I'"(" ",-"""'J. -.1Jssf /%f'I\iA. What is the longitude and latitude location of the road intersection at Buena VistaLj4 41o 110" \,Zs0t.s' H1-"i :'1.iS''- ,',/l.': "g O /1'5W-PtB. What is the lowest point of elevation represented on this map? )50C. What is the maximum relief.g.4P I'2-fYll' !t/I'Y\;J [it't/;il
D. What is the azimuth bearing FROM Davidson Hill TOWARDS Buena Vista?O'bOoE. What is the quadrant bearing FROM Buena Vista TOWARDS Davidson Hill? S 5()'N13)A. What is the nature of the topographic slope in the vicinity of the town of Monmouth? il \'i c.;)\O?irl'DC. What is the local relief between WOU and the Willamette adjacent to Independence?c:. 10 - \ 50 - (o()f' D. Is the outline of the topography east of Independence relatively arcuate or irregular in outline?\ r\e V \0- E. What processes might, have formed the pattern in D above?p:y.:::tb\ b\,-\ \ OJ,d G i des ,)C l.}I):'rt-.0b1c h 1\ c)lor- t' ')14) Examine the cultural activity immediately north of Monmouth and Independence.A. Write a brief assessment of the potential for environmental degradation to the surface andgroundwater of this area. List three types of water quality degradation (i.e. contamination) problems",:, \ rJe,Q.: 1'1 J,. .'·hY) \ .1,-'" \,I.C"that may exist in this area.SO\J'fCe ofelWlfuf\yrt\ITC-IO'(\ IJ\ {'\CV\\\,;YC'.,l.V'2,e \,'. t\-)t \, '1 tlne,V"U\1 I ' II:) n'(\v;ACC"1UT ''j.I'C."\,-,I ",VI. 1\0-:,\ \r-.,e.;\V\ \"SCAS o.lM""lCV\iu.-e. ',)J,,(ir· he) ,\(# i-v-,erhe -1,0, r ,;-{'O'\'('\'-)I(,'cIr,)\Y\'''.rYlO-I/1 O(J»"I' ie, P,(i"'l :: nt'\ ,.f',"I/,IS \-OM Jl Y\A \(')' -'i\'/)t,*, /I p::lr t' :ie"18. Determine the elevations of the following locations:A. Wigrich z.toO-t\-·B. Oak Hill (SC) 4- l.?.( C. Dicker Reservoir (NE) y.'SO-\4 D. Davidson Bridge (SC) IlYO\'-t19. Draw a topographic profile along a line connecting Oak Hill (SC) to Vitae Springs. Use a horizontalscale of 1 in 4000 Ft, and a vertical scale of 1 in 333.33 ft (see attached profile paper). A. Determine the minimum slope grade represented on the profile in percent.I;", wtlho.Me ",er to 1': 1)\\''1 13 ' tJucthf nB. Determine the maximum slope grade represented on the profile in percent.q o l? Jf\\"" O-f\NO,(,\-W: rfllov;t"t' Sl'n 'i sC. Where are the areas rilost likely associated with flooding?\N,\\;lAno-e\ft R\lt'" c-dJ( (C/,tD. The vertical exaggeration of a profile is calculated by: VE H scale / V scale;Calculate the vertical exaggeration represented on the attached profile.2
Topographic Profile from Oak Hill to Vitae Springs, Monmouth, OR Quad.Oak Hill.Jen 500« :400oc 30010 (])WVitae Springs600!---'"""- -.-0200100,IIcCi.i:'i,.:-y?I.;.;;:.!' - .,I ,;j c.II tII:z:::iITIHorizontal Distance in Feet (each tic Horizontal Scale: 1 in 4000 ftVertical Scale: 1 in 333.33 ft V.E. HN C:lMJu:geomorph:monbiankgrf.01 33 tt/ - V. 33 3 ,".",I./':--- /\0 /'""/y;rIJIII 2000 ft)IIII
Primer on Solving Quantitative Style Word Problems in Physical Science and Geology Study Technique: Follow the step-by-step problem solving method outlined below; review the attached example problems and solutions; practice repetitively and compare your answers to key. (1) Carefully read the word problem
General Problem-Solving Steps Questions in the Quantitative Reasoning measure ask you to model and solve problems using quantitative, or mathematical, methods. Generally, there are three basic steps in solving a mathematics problem: Step 1: Understand the problem Step 2: Carry out a strategy for solving the problem Step 3: Check your answer
3.3 Problem solving strategies 26 3.4 Theory-informed field problem solving 28 3.5 The application domain of design-oriented and theory-informed problem solving 30 3.6 The nature of field problem solving projects 31 3.7 The basic set-up of a field problem solving project 37 3.8 Characteristics o
can use problem solving to teach the skills of mathematics, and how prob-lem solving should be presented to their students. They must understand that problem solving can be thought of in three different ways: 1. Problem solving is a subject for study in and of itself. 2. Problem solving is
Combating Problem Solving that Avoids Physics 27 How Context-rich Problems Help Students Engage in Real Problem Solving 28 The Relationship Between Students' Problem Solving Difficulties and the Design of Context-Rich Problems 31 . are solving problems. Part 4. Personalizing a Problem solving Framework and Problems.
The Problem Solving Inventory (PSI) [8] is a 35-item instrument (3 filler items) that measures the individual's perceptions regarding one's problem-solving abilities and problem-solving style in the everyday life. As such, it measures a person's appraisals of one's problem-solving abilities rather than the person's actual problem .
Problem Solving Methods There is no perfect method for solving all problems. There is no problem-solving computer to which we could simply describe a given problem and wait for it to provide the solution. Problem solving is a creative act and cannot be completely explained. However, we can still use certain accepted procedures
THREE PERSPECTIVES Problem solving as a goal: Learn about how to problem solve. Problem solving as a process: Extend and learn math concepts through solving selected problems. Problem solving as a tool for applications and modelling: Apply math to real-world or word problems, and use mathematics to model the situations in these problems.
CURRICULUM VITAE : ANN SUTHERLAND HARRIS EDUCATION B.A. Honors (First Class) University of London, Courtauld Institute 1961 European art and architecture, 1250-1700 PhD. University of London, Courtauld Institute 1965 Dissertation title: Andrea Sacchi, 1599-1661 EMPLOYMENT 1964-5 Assistant Lecturer, Art Dept., University of Leeds. 1965-6 Assistant Lecturer, Barnard and Columbia College. 1965-71 .
