{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 0 128 0 1 0 0 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 0 128 128 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 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 260 50 "High School Modul es > Algebra by Gregory A. Moore " }}{PARA 3 "" 0 "" {TEXT -1 4 " \+ " }{TEXT 259 32 "Rate-Time-Distance Word Problems" }}{PARA 0 "" 0 "" {TEXT -1 90 "\nAn exploration of the method of setting up and solving \+ rate/time/distance word problems.\n" }}{PARA 0 "" 0 "" {TEXT 261 153 " [Directions : Execute the Code Resource section first. Although there \+ will be no output immediately, these definitions are used later in thi s 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(plo ts): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 374 "RateTableEmpty := proc(name1, name2) \n \n local a, b, rt, M, equation;\n rt := cr ; #(a*ar + b*br)/(a+b);\n a := x; b := c-a;\n \+ \n M := array( [ [``, `Rate *`, ` Time`,` = Distance`], \+ \n [ name1, `?`, `?`, `?` ], \n \+ [ name2, `?`, `?`, `?` ] ]);\n \n \n end proc:\n\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 316 "R ateTableRT := proc(name1,r1,t1,name2,r2,t2) \n \n local \+ a, b, rt, M, equation;\n \n M := array( [ [``, `Rate *` , ` Time`,` = Distance`], \n [ name1, r1, \+ t1, r1*t1 ], \n [ name2, r2, t2, \+ r2*t2 ] ]);\n \n end proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 316 "RateTableRD := proc(name1,r1,d1,name2,r2,d2) \+ \n \n local a, b, rt, M, equation;\n \n M := arr ay( [ [``, `Rate *`, ` Time`,` = Distance`], \n \+ [ name1, r1, r1/d1, d1 ], \n [ n ame2, r2, r2/d2, d2 ] ]); \n end proc:\n\n" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 313 "RateTableTD := proc(name1 ,t1,d1,name2,t2,d2) \n \n local a, b, rt, M, equation;\n \+ \n M := array( [ [``, `Rate *`, ` Time`,` = Distance`] , \n [ name1, d1/t1, t1, d1 ], \n [ name2, d2/t2, t2, d2 ] ]);\n \n end proc:" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 13 "1. The Set-U p" }}{PARA 0 "" 0 "" {TEXT -1 199 "\nThe common thread to setting up t hese problems is to create a table to put the various knowns and unkno wns. Usually this problems involve two trains, cars, planes, runners, \+ or other moving objects.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "RateTableEmpty( train1, train2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "RateTableEmpty( `1st car`, `2nd car` );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "RateTableEmpty( plane1, plane2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "RateTableEmpty( `John`, ` Jane` );" }}}{PARA 0 "" 0 "" {TEXT -1 123 "\nNext, we'll insert inform ation into the various slots. If we knew the rates and times, we would have something like this :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "RateTableRT( car1, 50, 3, car2, 65, 2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "RateTableRT( `John`, 5, 3/2, `Jane`, 4.5, 2 );" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 35 "2. Same Distance - Different Rates" }}{PARA 0 "" 0 "" {TEXT -1 2 "\n " }{TEXT 256 11 "Problem 2.1" }{TEXT -1 179 " : Two cars drive from M udville to Sandville and arrive at the same time. The first car goes a t 52 mph, and the second car, which leaves 2 hours later, goes at 65 m ph. \n " }{TEXT 263 2 "A." }{TEXT -1 53 " Find the time that \+ the first car travels.\n " }{TEXT 264 2 "B." }{TEXT -1 104 " \+ Find the distance between the two cities\n\nFirst set up an empty char t (if doing this problem by hand).\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "RateTableEmpty(car1, car2);" }}}{PARA 0 "" 0 "" {TEXT -1 63 "\n\nWe can make a wild guess - which will turn out to be \+ wrong. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "RateTableRT(car1 , 52, 3, car2, 65, 2);" }}}{PARA 0 "" 0 "" {TEXT -1 177 "\nTo solve th e problem, we let t be the unknown time that car1 drives. We can then \+ fill in the times and rates for both cars. The distances are computed \+ as the products of these." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "RateTableRT(car1, 52, t, car2, 65, t-2); " }}}{PARA 0 "" 0 "" {TEXT -1 181 "\nSince the two expressions for distance refer to the same dis tance, they are equal. This means that we have an equation that we can solve - to get t. After getting t, we can find d." }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 37 "52*t = 65*t - 130; t = solve( %, t);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "d = 52*10;" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 42 "3. Same Distance - Different Rate and Tim e" }}{PARA 0 "" 0 "" {TEXT -1 2 "\n " }{TEXT 262 11 "Problem 3.1" } {TEXT -1 144 " : Two planes fly 1,960 miles. The second plane travels \+ 98 mph faster but takes 1 hour less time. Find the rate and time of th e first plane.\n " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "RateT ableEmpty( plane1, plane2);" }}}{PARA 0 "" 0 "" {TEXT -1 31 "\nIf we t ake this job, we get :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "R ateTableRT(car1, r, t, car2, r+98, t-1);" }}}{PARA 0 "" 0 "" {TEXT -1 101 "\nBoth of the expressions for distance are equal to 1,960. This g ives two equations with two unknowns." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "EQ1 := r*t = 1960;\nEQ2 := (r+98)*(t-1) = 1960; " }}} {PARA 0 "" 0 "" {TEXT -1 112 "\nSolve each of the equations for r. The n equate these solutions, because both of them are equal to r, and sol ve." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "solve(EQ1,r); solve(E Q2, r);\nEQ3 := % = %%;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "solve(%,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "t = 5;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "r = 1960/5;" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 12 "4. Same Time" }}{PARA 0 "" 0 "" {TEXT -1 2 " \n" }{TEXT 258 12 "Problem 4.1:" }{TEXT -1 496 " A bicyclist and \+ a rollerblader travel for 3 hours. The bicyclist travels twice as fast and ends up 2 miles farther. How far did the cyclist travel?\n\nThe k ey thing is to put the right expressions in the right places. The rate and distance of the bicyclist are both expressed in terms of the info rmation about the rollerblader. So we should let r = the rate of the r ollerblader, and d = the distance of the rollerblader. Then we can exp ress the rate and distance of the cyclist relative to those." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "RateTableRD( bicyclist, 2*r, d+2, rollerblader, r, d);" }}}{PARA 0 "" 0 "" {TEXT -1 50 "\nThe two \+ expressions for time are both equal to 3." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "2*r/(d+2) = 3; r/d = 3; \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "solve(%%, r); solve(%%,r);" }}}{PARA 0 "" 0 "" {TEXT -1 204 "\nWe can find the d, the distance travelled by the rolle rblader by equating these two expressions for r, and solving this. The n to answer the question, we need to add 2 to get the distance for the cyclist." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "d = solve( % = \+ %%, d);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "d + 2;" }}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 12 "5. S ame Rate" }}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 257 9 "Problem :" } {TEXT -1 137 " Rick and Steve both run at the same rate. Steve can run 30 miles if he runs four hours longer than Rick runs 18 miles. Find t heir rate.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "RateTableTD( Rick, t, 18, Steve, t+4, 30);" }}}{PARA 0 "" 0 "" {TEXT -1 27 "\n\nHe re are other examples. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "1 8/t = 30/(t+4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "t = solv e(%, t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "r = 18/6;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT 265 36 "\n \251 2002 Waterloo Maple Inc " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 1" 23 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }