  @qDISTANCE TUTORIAL -- PART 3. Here is a sample distance problem involving two objects. Remember to draw diagrams to show what is happening.@dwhite&d(0, )@jJoe and Sue leave home at the same time, travelling in opposite directions. If Joe goes 30 mi/hr and Sue goes 40 mi/hr, how far apart will they be in 3 hours?@dcars@rREAD&d(0,Read the whole problem. What are the facts?)&d(0,\f08What is Joe's Rate of Speed?\n\f08What is Sue's Rate of Speed?&qJoe goes 30 mi/hr and Sue goes 40 mi/hr&q)&d(0,How long does each person travel?\n&q3 hours&q)&d(0,What is being asked?&qHow far apart will they be&q)@rPLAN&d(0,Draw a diagram. On a piece of paper make a diagram that shows what is happening.)@dpart1&d(0,Joe and Sue begin at the same place\, going in opposite directions.&qleave home at the same time&q &qtravelling in opposite directions&q)@dpart2&d(0,After 1 hour: Joe has gone 30 miles, and Sue has gone 40 miles.)@dpart3&d(0,After 2 hours: Joe goes 30 miles more, and Sue goes 40 miles more.)@dpart4&d(0,After 3 hours: Joe goes another 30 miles, and Sue goes another 40 miles.) &d(0,Equation Idea. Use the diagram to sketch an equation that relates the facts to what is being asked.)&d(0,Let Dj = Joe's distance\, and Ds = Sue's distance.)&d(0,The Equation Idea will relate Dj (Joe's Distance) and Ds (Sue's Distance) to the Total Distance.)&d(0,Joe and Sue are going in different directions. So\, the Total Distance is the sum of the distance each travels.)&d(16,                            )@pWrite an Equation Idea that expresses the relation between Dj, Ds and Total.@hThe Total distance is the sum of the distance Sue and Joe travel.@h  Joe's        Sue's\nDistance     Distance\n  `Dj     +     Ds     =    Total'@i(16,c0,Dj+Ds=Total)@pOne answer is: `Dj + Ds = Total'. If yours is not equivalent, you should change it.@hSince Joe and Sue are travelling in opposite directions, the Distance between them is the sum.@h  Joe's	      Sue's\nDistance     Distance\n  `Dj     +     Ds     =    Total'@i(16,c0,Dj+Ds=Total)@rDATA@dg04&d(1,U/Meas)&d(4,Total)&d(5,Rate)&d(10,Time)&d(15,Dist)&c(2,Joe's Car)&c(3,Sue's Car)&c(20,Dj + Ds = Dt)&d(0,The problem now reduces to determining the distance Joe travels and the distance Sue travels.)@pBegin by filling in the chart. Fill in the Unit of Measure for each quantity, starting with Rate.@hRate of speed in this problem is determined by the miles travelled in one hour.@hEnter `mi/hr' at the prompt and press the <Return> key.@i(6,c5,mi/hr)@pFill in the unit by which Time is measured in this problem.@hTime is commonly measured in seconds (sec), minutes (min), hours (hr), and years (yr).@hTime, in this problem, is measured in hours. Enter `hr' at the prompt and press the <Return> key.@i(11,c2,hr)@pFill in the unit by which Distance is measured in this problem.@hDistance is commonly measured in feet (ft), yards (yd), kilometers (km), and miles (mi).@hDistance, in this problem, is measured in miles. Enter `mi' at the prompt and press the <Return> key.@i(16,c2,mi)&d(0,Enter the facts from the problem into the chart. Start with the Time Joe and Sue will travel.)@pEnter the Time Joe will be travelling.&q3 hours&q@hThe problem asks how far apart they will be in 3 hours, so the Time Joe will be travelling is `3 hr'.@hEnter `3 hr' at the prompt, and press the <Return> key.@i(12,i,3)&d(12,3 hr)@pEnter the Time Sue will be travelling.&q3 hours&q@hThe problem asks how far apart they will be in 3 hours, so the Time Sue will be travelling is `3 hr'.@hEnter `3 hr' at the prompt, and press the <Return> key.@i(13,i,3)&d(13,3 hr) @pEnter Joe's Rate of speed.&q30 mi/hr&q@hJoe is travelling at 30 mi/hr. That is his `Rate of speed'.@hEnter `30 mi/hr at the prompt, and press the <Return> key.@i(7,i,30)&d(7,30 mi/hr)@pEnter Sue's Rate of speed.&q40 mi/hr&q@hSue is travelling at 40 mi/hr. That is her `Rate of speed'.@hEnter `40 mi/hr/ at the prompt, and press the <Return> key.@i(8,i,40)&d(8,40 mi/hr)@pEnter a variable for the unknown -- the Total Distance travelled by both Sue and Joe.@hUse a variable, such as `t', to represent the Total Distance travelled.@hEnter a variable, such as `t', and press the <Return> key.@i(19,i,&v)@rPARTS@pEnter an expression for the distance Joe travels, using Rate * Time. `30 * 3'@hJoe is travelling at 30 mi/hr for 3 hr. Use the Equation Idea:\nDistance = Rate * Time.@hRate * Time is 30 mi/hr * 3 hr. Enter `30 * 3'.@i(17,i,30*3)@pEnter an expression for the distance Sue travels, using Rate * Time. `40 * 3'@hSue is travelling at 40 mi/hr for 3 hr. Use the Equation Idea:\nDistance = Rate * Time.@hRate * Time is 40 mi/hr * 3 hr. Enter `40 * 3'.@i(18,i,40*3)@s@rWHOLE&d(20, )@pNow, substitute these values in the Equation Idea: Dj + Ds = Total.@hDj = (30 * 3), Ds = (40 * 3), and the variable `&v' represents the Total Distance.@hEnter `(30 * 3) + (40 * 3) = &v',\nor `90 + 120 = &v'@i(20,i,90+120=&v)@rCOMPUTE@pUse the Calculator to solve the equation for `&v' (Total Distance).@hThe Calculator solves equations for you and shows steps in the solution.@h90 + 210 = &v. So, enter `210 = &v'.@i(20,i,210=&v) @rCHECK@pReread the problem. Enter your answer in the chart.@hSubstitute the value of `&v' in the chart.@hEnter `210'.@i(19,i,210)@r&d(0,This completes the Tutorial. You are now ready to solve problems on your own. Choose Distance Problems, Level 2.) |