The Public Transportation Considerations
challenges for high school math classes:
examining the mathematics of a social and environmental
Problem Statement :
I was riding the train to work at the early part of rush hour. I
looked back through the car and noticed that there were 22 rows of
seats each averaging 3 people per row. When I got on I noticed that
our train was composed of three cars and I had moved towards the
least crowded car.
During the time we sat riding into Center City I mused, how would
eliminating the train and turning all these riders into regular
automobile commuters effect the morning traffic? What other things
would this change effect?
- List all the ways increased traffic will effect the roads and
city that you can think of. Use any mathematical means you can to
determine the results of turning rail commuters into automobile
commuters will have for the items in your list.
- List all the environmental effects of automobiles that you can
think of. For each idea you listed, determine how eliminating the
trains would effect this aspect of the environment.
- List all the social and health effects that increased traffic
might have. Determine how big an impact the increase in traffic
will have on these parts of society.
- What other considerations can you think of that are not
- Take the simple estimate I made for the train I was riding,
and estimate how eliminating that train would impact the city.
- Recognize that at any given time SEPTA has 16 train-lines
running at once (eg.: R8 represents a train coming in from Fox
Chase and one from Chestnut Hill.) Estimate how this would impact
- Contact SEPTA to determine how
many passengers use rail to commute into the city during business
hours on a typical week day. (DVARP
- Another source of information) Use traffic data as a
Hints for math classes
- Many parts of this problem are geometry problems of comparing
areas. Most of those areas may be approximated with rectangles
- Some parts of this problem are ratio or algebra formula
problems (eg: where can you find a formula for the emission of
Problem Statement 
SEPTA receives a subsidy from the federal government. Some people
consider this unfair. However, the auto industry receives indirect
subsidies from all levels of government. The railroads must maintain
their own tracks, and purchase new land for tracks if they want to
expand. In contrast, federal, state, and local governments, all buy
land for roads, and maintain roads at taxpayers expense.
What then would constitute a fair system of subsidies, so that
neither automobile commuters or train commuters would be receiving an
unfair share? Determine what you think would be fair.
Problem solving considerations:
- What will your definition of "fair" be? (eg.: dollars per
passenger, dollars per mile, other?)
- How will you find out what the current subsidy is?
- What calculating will you need to do to determine the fairness
of the money being spent?
Problem Statement 
SEPTA inherited the bankrupt Reading Lines and Pennsylvania Lines.
These railroads were designed for the economy of the turn of the
century and functioned rather well until about 1960, when
technological and cultural changes moved the population centers and
industrial base away from the rail lines. A prime example of this is
the Newtown line, once used to bring farm-goods into the city, it now
meanders through suburban housing developments in a direction that
few desire to travel.
To address many of the issues considered in problem 1, we should
design a rail road system that fits the modern economy. Can we design
a cost effective commuter system that will actually serve the modern
commuters? If you do not live in the area served by SEPTA, think of a
place near you that would be well served by light rail.
Problem solving considerations & suggestions
- Think of and list the needs of modern commuter - workers,
consumers, and tourists. What qualities will a modern rail system
need to serve these people well? What should rail give them access
to? Are there things that rail should avoid? That is, how will you
- How will you minimize the costs? Your rail line will not be
profitable if it costs too much to build or operate. List the
things that you must consider to minimize your costs.
- Use a map server like
mapquest. Determine where
people need to go.
- Now design a rail system that will serve your area.
- Hints from the past: At least one rail road company put
amusement parks at the end of some of its lines to convince people
to ride. Most used their tracks for both freight and commuters.
I will be glad to hear from any classes that produce significant
results for any of these challenge problems. Towards the end of the
school year, I would be glad to upload your finding giving credit to
Let me know about your results