Help understand wording of question

[L²Cc]

Homework Statement

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 positive 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?!

Homework 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.

The Attempt at a Solution

?? I think I attempted at a solution above.

Thank you! (and sorry for making the thread so (unnecessarily?) lengthy)

 

[EnumaElish]

The question that follows asks "at what times did the river flow at that rate?"

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.

 

[L²Cc]

Using a graphical app, I measured the slope at every point and none equal the average rate??!

Thank you.

 

[Integral]

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?