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# Windows on a Subway

## Question

Hey everyone, this is not so much a standard brainteaser as it is a real world application of logic and math. Without further ado-

Question:

How would you calculate the total surface area of all the windows on a typical New York City subway train?

The steps you would take to answer this question matter more than the actual number.

This is how I would approach the question:

Identify a subway train that is representative of a "typical NYC subway train."

Identify the different types of windows on the body of that train, eg. door windows, side windows, smaller side windows.

Found out how many of each type of window a single car contains.

Estimate the respective surface areas of each type of window.

Calculate the surface area of all the windows on a car.

Find the average number of cars on a single train.

Estimate the surface area on the head of a train (assuming that it's different from the cars that make up the body).

Estimate the surface on the back.

Surface Area of Windows on a car * number of cars + surface area of the back car of the train + surface area of the head of the train= total surface area of the train?

Does this logic seem sound? Would you approach the problem differently?

## 3 answers to this question

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I don't know if there's a trick here like "the windows on subs are actully a non-glass polymer" or something, but there are 13 different kinds of cars presently used by the NYC CTA for the subway system. The MTA will finally release the R211 this year, so the style of cars is constantly changing (especially with the 179's coming out).

So....Yes. I would use your steps above.

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Several ways to solve this one:

First, find out how much soap is used annually by NYC train authority to clean windows, estimate total fleet size, frequency of cleaning schedule, soap needed per square foot, number of windows per train - and you got your answer

Second, windows are held by rubber caulking. They tend to get brittle over time and need replacement, FInd out how many feet of rubber caulking was purchased by NYC train authority ( probably the same person who gave you the soap used), estimate lifetime replacement cycle of rubber caulking, number of trains in system, number of windows and with the circumference get the total area

Third, train windows shatter rather often. Estimate number of shatters/year/train. Ask the same guy at NYC train authority how much glass they buy each year, use the same info as above and you'll get the glass area

Fourth, Google Bombardier's web site, ( the manufacturer of NYC trains) , find the right - or approximate picture of train in web site. Web site probably also gives typical dimensions of trains and thus estimate window size ( # of windows too). Alternative, estimate window size by comparing known entities in pictures ( eg.. human being, lamp post, etc. etc) and work from there to get window dimensions. You can probably get the exact # of windows from one of these nice sales pictures Bombardier has in their web site

Finally, go to Linkedin, pose the question - who works at PPG ( the glass manufacture of these windows) and get him/her to provide the right area per window, Estimate # of windows from above other options and get the necessary square footagekarchimex

Edited by karchimex
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I wonder whether the OP envisioned lateral thinking answers to the question.

Karchimex [welcome to the Den, btw] certainly found a few!

Reminds me of the ways to measure the height of a building, using a barometer.

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