Distance Time Rate Worksheet Welcome to Math 111 Algebra

							            Welcome to Math 111
     Algebra in Business and Economics
             Instructor: Alexandra Nichifor


                    Class Website:
  http://www.math.washington.edu/~nichifor/111F06.htm


Please pick up a copy of the syllabus and today’s
                    handout
      Worksheet 1:
Speed as a Rate of Change
                                    Time t      Distance D
                                    (minutes)   travelled (miles)
                                                after time t
                                          0          0
                                         10         120
                                         20         170
                                         30           180
                                         40           180
Q?: How far did the rocket travel
     from 50min to 60min?                50           205
                                         60           280
      280-205=75
                                         70           430
A: 75 miles                              75           550
                        Delta Notation:

• Greek letter Delta:               is shorthand for
“the change in”
 Example:

  How far did the rocket travel from 50min to 60min?

           D  280  205  75 miles
  (over a duration of t  60  50  10 min)
Q: What was the average speed of the rocket from
             t=50 min to t=60 min?
                                                  Shorthand
                                                  (=change
                                           D       in…)
    average speed = Change in distance 
                     Change in time        t


      D 280  205 75
 AS                   7.5        miles per minute
      t   60  50   10
                      On the graph:
           Moral: Average Speed (AS) from time t1 to time t2
=slope of the secant line thru the graph of the distance at points t1 & t2




                                                            Rise

                                                         D  75




                                           t  10
                                                         Run
A rate of change is a measure of how fast a
  quantity is changing with respect to time

Examples?
VIP Example: average speed is a rate of change of distance.



                                        D
   average speed = Change in distance 
                        Change in time       t


 In general:
                                                        Blah
 Average Rate of Change of Blah =
                                    Change in Blah
                                                     
                                                         t
                                    Change in time
                     Types of Rates of Change:


                                                  Actual (Instantaneous)
    Average Rate of Change
                                                  (will study in Math 112)

                                             Example: Actual speed,
                                             as read off a speedometer


         Overall                Incremental
  (from t=0 to later time)    (from t=a to t=b)

       Example:                    Example:
Average Trip Speed (ATS)      Average Speed (AS)
         distance so far D         change in distance  D
   ATS                      AS                    
           time so far    t          change in time    t
• Note: An overall rate of change (such as ATS) is
  a special case of an incremental rate of change.
  that is, one in which the initial time t1=0.
• Question: How do we measure the ATS on a
  graph of distance?
  For example, on our handout, what was the ATS
  over the first hour?
• Answer: Compute the slope of the line from the
  beginning of the graph (t1=0) to t2=60 min.
                                                           ATS=
                                                          Slope of
                                                          Diagonal
                                                            Line




                                                          Rise=350




Tip: Can pick any two points on this line to compute the slope!

                           Run=75
Answer: ATS over the first hour = 350 / 75 = 4.67 mpm = 280 mph
Note: Using the original two points: 280 / 60 =4.67 mpm
                  …To be continued on Friday…


Homework for Friday:

   1. Familiarize yourself with the class rules by carefully
      reading the syllabus and the class website.

   2. Print the Lecture Handouts (and bring to class!)

   3. Get the text, a ruler, and a scientific calculator.

   4. Read and do the problems in the Prologue.

   5. Start working on Worksheet 1.