Fire Services and Mathematics

Joseph Malkevitch
Mathematics Department
York College (CUNY)
Jamaica, New York 11451

email:

malkevitch@york.cuny.edu

web page:

http://york.cuny.edu/~malk/

Here are some sample problems that can serve as part of a problem solving environment which reviews arithmetic, algebraic, statistical, modeling, and reasoning skills, and which relates to issues of urban fire department services.

Note: In many of the problems below part of the point of the problems is to see how hard it is to get data for relatively simple, interesting, and important questions.

1. a. How many firehouses are there in each of the five boroughs of New York City?

b. What is the population of each of the five boroughs of New York City?

c. What is the area of each of the five boroughs of New York City?

2. What is the number of people per firehouse for each of the boroughs?

3. What is the number of people per firehouse citywide?

4. What is the relative and absolute difference between each pair of boroughs for people per firehouse?

5. What is the relative and absolute difference between the boroughs and the city wide value of people per firehouse?

6. What information might you need to try to determine if you wish to determine if there is "equitable" coverage for the different boroughs of the city?

7. What is the percentage of the total population of NYC is in SI?

8. What percentage of the area of NYC is accounted for by Queens?

For some additional problems it will be convenient to use the diagram below (Figure 1) which represents a section of a city. Assume all the streets are two way streets.

Figure 1

Assume there are firehouses at C and F, a police station at A, a hospital at B, a supermarket at D, and a school at E.

9. Assuming all blocks in Figure 1 are of equal length one, and one introduces a coordinate system so that B has coordinates (0, 0), what would be the coordinates of A, C, D, E, and F?

10. What is the crow flies distance between the two firehouses?

11. What is the "driving distance" between the two firehouses.

13. If a medical emergency occurs at (4,5) what distance would a helicopter have to travel from the hospital to get there?

14. If a medical emergency occurs at (4,5) what distance would an ambulance have to travel from the hospital to get there?

15. List the coordinates of all points in Figure 1 with integer coordinates which are 3 units away to drive from E.

16. If a fire occurs at (4, 2) engines from which firehouse should respond?

17. If a fire occurs at (7, 3) engines from which firehouse should respond?

18. If it takes 39 seconds to drive a block how long will it a police car to drive to (5, 5)?

19. If the city shown in Figure 1 extends to other points (including those with negative integer coordinates), how far is it from the supermarket to:

a. (-3, 5)

b. (-11, 12)

c. (-9, -4)

d. (13, -11)

e. (-12, -6)

20. How many miles to a gallon of gasoline does a "typical" fire engine get?

21. What is the mean salary of firefighters who work for NYC?

22. What is the median salary for firefighters who work for NYC?

Here are some less clearly defined problems and projects that would require students to come to grips with various mathematical issues:

I. How well paid are firefighters in New York City compared with other government workers in the City and firefighters in other cities?

II. There are claims that "the FDNY is the least racially and gender diverse major department in New York City and one of the least in the country." Can you find data that supports/contradicts this claim?

III How does the size of the FDNY compare with the size of fire departments in other cities?

IV How might one measure whether or not the fire coverage the city provides in Queens and SI are equal?

V. What determines the number of fires in different areas of a city? The age of the housing stock? The density of the population? The affluence of the people who live in a particular neighborhood? Whether the neighborhood is industrial versus residential?