I started with total track miles, which felt like the right anchor, then tried to work backwards through headways and average train length.
Break the problem into supply and demand: first estimate the number of trains needed to meet peak demand, then adjust for off-peak periods. Use a top-down approach starting with NYC population and subway ridership statistics, then work down to train frequency and capacity.
Pro tip: State your assumptions clearly and round numbers to simplify calculations; interviewers care more about your structured thinking than the exact number.
Ask if the estimate should be for peak hours, average across the day, or a specific time. Confirm whether 'trains' includes all lines and whether they are in service or including those in depots.
Use known NYC population (~8 million) and assume a percentage use the subway daily. Alternatively, recall that NYC subway daily ridership is about 5-6 million on weekdays.
Estimate train capacity: a typical subway train has 8-10 cars, each car holds ~100-150 passengers (crush load). So capacity ~1000-1500. Assume average load factor (e.g., 50-70% during peak, lower off-peak).
Divide hourly ridership by average passengers per train to get trains per hour. For peak hour, ridership might be ~500,000; with 1000 passengers per train, that's 500 trains per hour across all lines.
Estimate average trip duration (e.g., 30-60 minutes). If 500 trains per hour and each trip takes 1 hour, then 500 trains are operating at any given time. Adjust for off-peak by averaging over 24 hours or focusing on peak.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.