(60, 180, 587.5)
THE MATH TRAIN
1. How long is the railroad track?
Method A) Place a piece of string on the OLAP map along the railroad track.
Now place the string on the map along the axis.
Method B) Use a compass or a divider to count the number of short divisions
along the track.
2. How fast does the train go?
Method A) Determine the distance of a section of the track.
With a watch, time how long it takes the train to cover this section.
Now, apply the formula.
Formula: D = r t
Where D = distance or section length,
r = rate (speed)
and t = time
Method B) Stay in the station and determine the time it takes the train to
leave, go around once and stop timing when it leaves again. Then use the above D = r t
formula again with D = the length of the entire track and t = the total loop
time.
3. Why are the rates so different for question 2 Method A and Method B?
4. Considering your answer to question 2, what is the maximum speed of
the train in any short interval over the entire track? How could you
find and check your answer?
5. What area is enclosed by the train track?
Look for a lower bound, a number for the area, that you are certain the
train track includes.
Look for an upper bound, a number for the area that includes the train track?
Now work together in a group to bring these numbers closer together. But, be
sure the upper bound covers the train track area and the train track area
covers the lower bound area.
How would you find one number to represent this train track area?
6. How could one make the train go faster over a longer loop of track yet
enclose a smaller area?
FASTER THAN A LOCOMOTIVE
If a person walks 3 miles an hour, how long will it take him
or her to walk the distance of the railroad track?
In the time it takes this person to walk the distance of the tracks
one time, how many more times will the train go around the park?
SOME SECTIONS OF THE TRACK REPRESENTED BY STRAIGHT LINES
Consider using straight line equations y = m x + b, y - y1 = m ( x - x1) or
(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1) to write the map location for sections of
the
railroad track. One person used the slope formula m = (y2 - y1)/(x2 - x1)
with one of the first two
equations and had the following method:
1. Extend a line off a section between two points of a coordinate map's RR track to the
nearest coordinate line.
2. Observe the point of intersection of this extended line and the coordinate
line.
3. Guesstimate the coordinates for the point of intersection to get the
ordered pair.
4. Repeat steps 2 and 3 in the other direction to get a second ordered pair.
5. Plug the ordered pairs into the slope definition, m above, to get the
numerical value of the slope.
6. Use the point slope form, y - y1 = m ( x - x1) together with one of the points
and the slope to arrive at the slope intercept form, hence a final equation.
Here are some results for secant or tangent lines on the Northern semiring.
EQUATION x interval
y=-(19/36)x+746 [-36,0]
y=-(51/116)x+689.28 [360, 476]
y=(16/1449)x+621.05 [-729, -720]
y=(163/30)x+4177.3 [-813, -783]
y=(62/23)x-2318.3 [809, 832]
y=-0.0843x+70 [825, 830]
y=-0.1824x+155 [810, 825]
y=-0.2644x+230 [780, 810]
y=-0.3011x+280 [740, 780]
y=-0.36x+360 [690, 740
y=0.78x+790 [-660, -600]
y=-.53125x+740 [0, 480]
y=4.5472x4010.6304 [-882,-723]
Graph these lines on the RR Track to see how close they represent the track line.
Let's look at the RR Track elevetions next time we get a chance.
This would be a great place to have some information on a Six Flags' steam engine.
Carrie Datillo,
Clay Gregorc, Jennifer MacMorran contributed to the RR Track secant and tangent line section.
Copyright © 1994 © 1996 with all rights reserved by William V. Thayer, Mathematics Department, St. Louis Community College at Meramec, 11333 Big Bend Blvd., St. Louis, MO 63122-5977, Telephone: 314 984 7866, Email: thayer@stl-online.net
Copyright of all Six Flags' rides and building
names herein belong to Six Flags(R) Theme Park