I started with reaction time per driver, then added acceleration lag, and tried to estimate the time gap between each car moving.
Break the problem into two phases: the time for the first car to start moving after the light turns green, and the time for the queue to discharge. Use a simple model where each car takes a fixed reaction time plus a headway to start moving, and account for acceleration and spacing to estimate total clearance time.
Pro tip: State your assumptions clearly and round numbers to make mental math easy; interviewers care more about your structured thinking than the exact answer. Also, mention that in reality, factors like driver behavior and vehicle types add variability, so your estimate is a baseline.
Confirm that the 100 cars are in a single lane and that the light turns green simultaneously for all. Assume typical car length and spacing, and that drivers react with a certain delay.
Estimate the time for the first car to begin moving (reaction time) and the additional time for each subsequent car to start moving (headway). Use a constant headway for simplicity.
Multiply the headway by the number of cars (or 99 if the first car's start time is separate) to get the time for the last car to start moving. Add the time for the last car to clear the intersection.
Estimate the time for a car to accelerate from stop to a typical speed and travel the length of the intersection plus its own length. Add this to the last car's start time.
Add the start-up delay, queue discharge time, and clearance time to get total time. Check if the result is reasonable (e.g., 30-60 seconds) and adjust assumptions if needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.