Estimate how many trains operate in the NYC subway.

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Estimate how many trains operate in the NYC subway.

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P · Answer 1 · 2020-07-17T19:53:13+0000

First, before answering this Google estimation question, I would like to make sure we're aligned on the exercise. A few questions:

By trains, you mean a set of train cars joined together? Or individual train cars? Train = Set of train cars.
By operating, you mean trains that took at least one ride on a given day? Or train rides? E.g. if a train does three two-way trips per day, should we count it as one train or 6 trains? It should count as one unique train.
What time period should I use? A week day.

Ok, let's start the estimation. Here are a few things I'd like to know:

Number of riders taking a subway train ride on an average day in NYC
Average number of train ride per day per rider
Average capacity of a train
Average utilization of a train
Average rides per day per train

# of trains operating in NYC = [Number of riders taking at least one subway train ride on an average day in NYC * Average number of train rides per day per rider] / [Average capacity of a train (in riders per train) * Average utilization of a train (in % of train capacity utilized * nr of rides per train per day]

Number of riders taking at least one subway train ride on an average day in NYC	Average number of train rides per day per rider	Average capacity of a train (in riders per train)	Average utilization of a train (in % of train capacity utilized]	# of rides per train per day
NYC population * % taking subway on a given day 10M * 30% = 3M	Return trip + some other addl trips 2.5 rides per day	Avg 6 cars, 80 max capacity per car: 480 riders per train = ~500	100% peak hours, 20% outside of peak hours (100%5hrs +20%15hrs)/20 hrs operating in a day = (5+3)/20 = 40%	Average 10 hours operating per day / 2 hours per ride ( + cleaning, changing driving engineer, etc) = 5 rides per train per day

# of trains operating in NYC = (3M * 2.5) / (500*.4*5) = 7.5 M / 1,000 = ~7.5k trains

This number seems high to me. I would guess that given we're not only talking about Manhattan, but NYC, there is a smaller % of population taking the subway every weekday.