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Help understand wording of question

  1. Oct 28, 2007 #1
    1. The problem statement, all variables and given/known data

    In the previous question, we're asked to determine the average flow rate from 00:00 on 28 October to 00:00 on 2 November, which I did by finding the slope connecting these two points. The slope is -1/6 and so the average rate is -1/6 cfs/hours. The question that follows asks "at what times did the river flow at that rate?" (the rate being -1/6 cfs/hours). I'm confused as to what they are asking, perhaps some clarification (and lead-ins) will help me answer the question.

    Here are the data values:
    The time is measured in hours past midnight, starting at 00:00 on 27 October. The flow is measured in cubic feet per second (cfs).

    Time Flow
    0 440
    6 450
    12 480
    18 570
    24 680
    30 800
    36 980
    42 1090
    48 1520
    54 1920
    60 1670
    66 1440
    78 1300
    84 1150
    90 1060
    96 970
    102 900
    108 850
    114 800
    120 780
    126 740
    132 710
    138 680
    144 660

    Another question asks "the river is controlled by a series of dams. During which days did the amount of flowing water increase?". The first curve (if you read below I explain why I have two curves) has a postive slope and is thereby increasing, suggesting that the flow rate is increasing as well. For this question, I simply found the area below the first curve by computing the definite integral where the lower limit is 0 and the upper limit is 54. But then I did the same for the second curve, and saw that the area below this curve is greater than that below the first???!! Does this mean that the amount of flowing water is greater below the second curve (although the curve is following a 'decreasing' trend). Hence, what are they exactly asking by this question?!

    2. Relevant equations
    Earlier in the assigment, we had to find the best fit of the points. I divided the data set into two sets, where the first set ends with the x value 54 and second set starts with the x value 54 as well, so that I ended up with two curves. One curve isn't very informative of the trend followed by the points.

    3. The attempt at a solution
    ?? I think I attempted at a solution above.

    Thank you! (and sorry for making the thread so (unnecessarily?) lengthy)
  2. jcsd
  3. Oct 28, 2007 #2


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    Science Advisor
    Homework Helper

    I think this is asking you to identify those days when the incremental rate = average rate.

    "During which days did the amount of flowing water increase?" I don't think this has anything to do with averages. Just identify those days when F(t) > F(t-1).

    How did you decide on 54? I'd estimate an overall best fit. There are actually stat. tests that help determine whether the data can justifiably be separated into sub-parts for separate curve estimations.
  4. Oct 28, 2007 #3
    Using a graphical app, I measured the slope at every point and none equal the average rate??!

    Thank you.
    Last edited: Oct 28, 2007
  5. Oct 29, 2007 #4


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    Staff Emeritus
    Science Advisor
    Gold Member

    How are you getting your average? It is not clear to me why you are finding the slope, isn't the aveage usually defined in terms of a sum divided by the number of data points?
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