What's my distance?

There is more than one way to solve this particular problem. Please feel free to suggest an alternate solution, IN ADDITION to the method I have requested. If you provide an appropriate alternate solution, I may be inclined to give additional bonus points!

Please provide an explanation other than "I put the data in my calculator and ran a program."

The velocity from a speedometer on a car was recorded over a one-hour time span. The results appear in the table below.

Time (min)

Velocity (mph)

Compute an approximation to the distance traveled by computing an Upper Riemann Sum, a Lower Riemann Sum, and then finding the mean of those two values. Please give the values of the two computed sums, in addition to your final answer, as part of your solution.

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What's my distance? Solution

The Upper Sum would be computed by the following:
30(5) + 50(10) + 50(5) + 45(5) + 45(5) + 30(10) + 45(5) + 45(5) + 40(5) + 50(5).

However, this answer must be divided by 60 to convert the minutes into hours, so we get a sum of 42.5.

The Lower Sum would be computed as follows:
25(5) + 30(10) + 40(5) + 40(5) + 25(5) + 25(10) + 30(5) + 30(5) + 30(5) + 40(5).

Again, divide this result by 60 to obtain 30.83.

The mean of these two sums is 36.67 mph.

An alternate method, that gives the identical answer, is to use the "Trapezoidal" Rule.

How fast does it change?

Moldy Growth

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