The Public Transportation Considerations

challenges for high school math classes:

examining the mathematics of a social and environmental issue

Written 2001

Formatted 2010


Problem Statement [1]:

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 pondered, 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?

Problem Considerations:

  1. 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.
  2. 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.
  3. 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.
  4. What other considerations can you think of that are not mentioned here?

Problem-solving levels:

  1. Take the simple estimate I made for the train I was riding, and estimate how eliminating that train would impact the city.
  2. 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 the city.
  3. 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 baseline ( data).

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 greenhouse gases?)

Related pages at this site




Problem Statement [2]

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:

  1. What will your definition of "fair" be? (eg.: dollars per passenger, dollars per mile, other?)
  2. How will you find out what the current subsidy is?
  3. What calculating will you need to do to determine the fairness of the money being spent?

Problem Statement [3]

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 could be well served by light rail.

Problem solving considerations & suggestions

  1. 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 maximize ridership?
  2. 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.
  3. Use a map server. Determine where people need to go.
  4. Now design a rail system that will serve your area.
  5. 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. Many suburban industrial parks were built along old rail right of ways. Can they still be used?

Closing comments:

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 your class.



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