{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 128 0 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 128 0 1 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 262 "" 0 1 0 128 128 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 128 128 128 1 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE " Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 261 49 "High School Modul es > Algebra by Gregory A. Moore" }}{PARA 3 "" 0 "" {TEXT -1 4 " " }{TEXT 260 18 "Work Word Problems" }}{PARA 0 "" 0 "" {TEXT -1 279 "\nO ne of the most difficult types of word problems is work problems. Thes e problems involve two people, two machines, or two processes working \+ together to accomplish a single task. However, by using Maple we can g et a better understanding of how these work and how to solve them.\n" }}{PARA 0 "" 0 "" {TEXT 262 153 "[Directions : Execute the Code Resour ce section first. Although there will be no output immediately, these \+ definitions are used later in this worksheet.]" }{TEXT -1 1 "\n" }} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 7 "0. Code" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 22 "restart; with(plots): " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 408 "WorkTogether := proc( a, b )\n local x, t, A , B, pa, pb, pta, ptb;\n\n t := solve( x/a + x/b = 1, x):\n A \+ := t/a; \n B := t/b: \n pa := polygonplot( [ [0,0],[A,0],[A,1 ],[0,1] ], color = gold, axes = none):\n pb := polygonplot( [ [A,0 ],[1,0],[1,1], [A,1] ], color = red):\n pta := textplot( [ 0, 1.2, a]);\n ptb := textplot( [ 1, 1.2, b]);\n display( pa, pb, pta , ptb)\n end proc:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 606 "Wo rkTogetherEarly := proc( a, b, c )\n local pc, x, t, A, B, C, pa , pb, pta, ptb;\n\n t := solve( x/a + x/b = 1, x):\n C := c/a; A := (1-C)*t/a; B := (1-C)*t/b:\n \n pc := polygonplot( \+ [ [0,0],[C,0],[C,1],[0,1] ], \n color = gold, axes = none):\n pa := polygonplot( [ [C,0],[C+A,0],[C+A,1], [C,1] ], \n color = gold, axes = none): \n pb := polygonplot( [ [A+C,0],[1,0],[1,1], [A+C,1] ], color = re d):\n pta := textplot( [ A, 1.2, a]);\n ptb := textplot( [ 1, \+ 1.2, b]);\n display( pc, pa, pb, pta, ptb)\n end proc:" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 19 "1. The General Idea" }}{PARA 0 "" 0 "" {TEXT -1 107 "It will help us have a better feel for what is going on, if we can invision the work done by each party. \n\n" }{TEXT 259 7 "P roblem" }{TEXT -1 1 " " }{TEXT 263 5 "1.1 :" }{TEXT -1 268 " Rick take s 3 hours to complete a job working alone. Stewart takes four hours. H ow long will it take if they work together?\n\nThe person who can comp lete the job in less time is actually the faster worker - the person w ho will get more done in the same amount of time.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "WorkTogether( 3, 4);\n" }}}{PARA 0 "" 0 "" {TEXT -1 129 "\nIf a person takes 10 hours to do the job, compared to \+ someone who can do it one hour, that first person gets fairly little d one." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "WorkTogether( 10, 1) ;\n" }}}{PARA 0 "" 0 "" {TEXT -1 67 "\nIt's even worse if the first pe rson takes 100 hours to do the job." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "WorkTogether( 100, 1);\n" }}}{PARA 0 "" 0 "" {TEXT -1 96 "\nBut it's the other way around if the first person takes an ho ur, while the 2nd takes 100 hours." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "WorkTogether( 1, 100);\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 31 "2. Solving Simple Work Problems" }}{PARA 0 "" 0 "" {TEXT -1 2 "\n " }{TEXT 256 13 "Problem 2.1:" }{TEXT -1 295 " Ri ck takes 3 hours to complete a job working alone. Stewart takes four h ours. How long will it take if they work together?\n\nRick works at a \+ rate of 1/3 job/hour, while Stewart works at a rate of 1/4 of a job/ho ur. If they both work for t hours, then this is how much work they wil l accomplish.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "t/3 + t/4 ;" }}}{PARA 0 "" 0 "" {TEXT -1 116 "If we take this expression, which \+ represents the amount of work they do, and set it equal to one whole j ob, we get :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "t/3 + t/4 =1 ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "t = solve( %, t);" }}} {PARA 0 "" 0 "" {TEXT -1 2 "\n\n" }{TEXT 264 13 "Problem 2.2:" } {TEXT -1 386 " A storage tank has two input pipes, A and B. Pipe A ca n fill the the tank in 20 hours by itself. Pipe B can fill the tank in 35 hours by itself. If both pipes are turned on at the same time, how long will it take to fill the tank?\n\nPipe A has a rate of 1/20 of a tank per hour, or t/20 of a tank in t hours.\nPipe A has a rate of 1/ 35 of a tank per hour, or t/35 of a tank in t hours.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "t/20; t/35;" }}}{PARA 0 "" 0 "" {TEXT -1 206 "\nIf add how much is accomplished by pipe A and how much by B, and add them together, we find out how much of the tank is full after t hours. In particular we want the sum of the output to equal 1 full tank." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "t/20 + t/35 = 1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "t = solve( %, t); ev alf(%);" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 49 "3. Graphic View of M ore Complicated Work Problems" }}{PARA 0 "" 0 "" {TEXT -1 2 " \n" } {TEXT 258 13 "Problem 3.1 :" }{TEXT -1 224 " Alanis can complete a job in 7 hours if working alone. Britany can complete the job in 10 hours if working alone. If Alanis works for 2 hours by herself, and then is joined by Britany, how much faster can the job be done?\n\n" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "WorkTogetherEarly( 7, 10, 2) ;" }}}{PARA 0 "" 0 "" {TEXT -1 64 "\nWhat if Alanis worked for 4 hours before Britany came on board?" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "WorkTogetherEarly( 7, 10, 4);" }}}{PARA 0 "" 0 "" {TEXT -1 66 " \nWhat if Alanis works for a full 6 hours, before Britany shows up?" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "WorkTogetherEarly( 7, 10, 6 );\n\n" }}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 53 "4. The General Idea of More Complicated Work Problems" }} {PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 257 13 "Problem 4.1 :" }{TEXT -1 333 " Alanis can complete a job in 7 hours if working alone. Britan y can complete the job in 10 hours if working alone. If Alanis works f or 2 hours by herself, and then is joined by Britany, how much quicker can the job be done?\n\nAlanis' rate is 1/7 job/hour. If she works fo r 2 hours at that rate she will complete this much of the job :" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "2 * (1/7);" }}}{PARA 0 "" 0 "" {TEXT -1 69 "\nThis is how much of the job remains to be done, when Britany starts." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "1 - %;\n " }}}{PARA 0 "" 0 "" {TEXT -1 109 "\nWhen graphing these lines, the be st and fastest method is to find the intercepts and then 'connect the \+ dots'" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "t/7 + t/10 = %;" }} }{PARA 0 "" 0 "" {TEXT -1 26 "\nHere are other examples. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "answer := solve( %, t);" }}}{PARA 0 "" 0 "" {TEXT -1 96 "\nCheck the answer by putting this number back \+ in. Here is how much of the job Alanis gets done :" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 21 "(2 + answer) * (1/7);" }}}{PARA 0 "" 0 "" {TEXT -1 42 "\nHere is how much of the job Britany does." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "answer * (1/10);" }}}{PARA 0 "" 0 " " {TEXT -1 132 "\nTogether, these two portions of the job should add u p to the entire job. If these are correct, we should find that they ad d to one." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "% + %%;" }}} {PARA 3 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 265 36 "\n \251 2002 Waterloo Maple Inc \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 1" 49 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }