Australian Gas Problem
- Many of you did this problem just fine, but some of you had some trouble, so let's see if this helps a bit. First, you should've gotten an answer of somewhere between about $5.50 and $6.00 per gallon (because both the price of gas and the currency exchange rate changes daily, you'll get a different answer depending on what day you did this). If you got something very different from that, please go back and check to see what you did wrong (and adjust your blog post accordingly).
- Second, keep in mind the conversion we're trying to do. You're trying to go from Australian Dollars per Liter (think of that as a fraction) to US Dollars per Gallon (again, think of that as a fraction). So you have two dimensions you need to change: from Liters to Gallons and from Australian Dollars to US Dollars. Try to figure out how to write your ratios so that works out for you (filling in the appropriate numbers from the links I gave you, as well as finding the conversion factor between gallons and liters).
Hopefully this helps some. If it still makes no sense to you, perhaps come in on an unscheduled hour on Tuesday and we'll go through it.
Walking Directions Problem
This weekend I'm asking you to figure out the walking directions given to each of our guests today, including the speed (rate) at which I asked them to walk. What complicates this a bit is that over the course of the 10 seconds they walked, I gave them different directions for different intervals (e.g., walk for a certain speed for so many seconds, then stop for so many seconds, then walk at a different speed for the rest of the time). Also, it's darn hard to follow the directions I gave them perfectly!
So, if you go to the spreadsheet (which I've now locked down because I think we have almost all the data entered - don't worry about it if you were one of the ones that didn't get your data in due to technical issues), you'll see the data we collected for each walk (that's on the first sheet named "Data"). Now if you click on the second sheet (named "Kolasa 1"), you'll see a graph of those data points (just like you would graph them by hand, but already done for you).
Here's an image of the Kolasa 1 graph.
Now you can do several things with the graph. You can just work with it on the screen, you can print it out and work with it, or you can even download an image of it like I did for this blog post and then work with it - whatever you find easiest. What you're trying to do is figure out the directions I gave Mr. Kolasa based on the graph. For this first graph it sure looks like the directions were to walk at a steady speed for the entire 10 seconds. (Note that we are missing some data points there in the middle, but the trend seems to hold).
So, how do we figure out the speed? We go back to our formula, which tells us that we figure out rate (speed) by taking the distance traveled divided by the time it took. In this case our "interval" is the entire 10 seconds (because it appears he didn't have any different directions along the way), so we can just look at his total distance (8 m) divided by his total time (10 seconds), and get a speed of 0.8 m/s.
So your answer (if you agree with my analysis) would be that his directions were to "Start at 0 meters and walk at a steady rate of 0.8 m/sec." (Which is not bad, since what I actually asked him to try to do was to walk at a slow, steady rate of 1 m/sec, so he got pretty close.)
Now you repeat this with the other five walks. But they are more complicated because the directions weren't the same for all 10 seconds, and they didn't always start at 0 m. So, for example, when you look at Kolasa 2, you might hypothesize that I told him to stand still for a while there in the middle (do you see it on the graph and/or in the data?).
So you're going to probably have 3 "intervals" to calculate for Kolasa 2. First, calculate his speed for the first 6 seconds, then his speed for the next 2 seconds, then his speed for the last 2 seconds (can you see that on the graph and/or in the data?).
Similarly, for Murphy 1, Murphy 2, Meredith 1, and Meredith 2, you'll have multiple intervals to calculate (and their directions got increasingly more complicated). Click on their sheets to get their graph and try to figure it out. So, see what you can come up with for the 5 walks (I basically did Kolasa 1 for you above) and we'll talk about it a bit on Monday.