Traffic-signal estimate: green time for 100 cars on a one-lane road

An interviewer gives you an estimation problem. A traffic light controls a road that has a single lane. Estimate how long the light needs to stay green so that 100 cars get through, state each assumption you make, and arrive at a final number. ```hint The queue does not move as one block Think about everything that happens between the moment the light turns green and the moment the 100th car reaches the stop line. ``` ### Clarifying Questions - Are all 100 cars already stopped in a queue when the light turns green, or do some of them arrive while it is green? - Does "get through" mean the last car crosses the stop line before the light changes, or that it fully clears the intersection? - What kind of road is it, a city street or a faster road, and what is the speed limit? - Are all the vehicles ordinary cars, or does the queue include trucks and buses? ### What a Strong Answer Covers - Clarifying what counts as getting through and whether the cars are already queued, before any arithmetic. - An equation that separates the start-up delay from the steady rate at which cars cross the stop line. - Labeled, realistic assumptions about car length, gaps, driver reaction, acceleration and speed on a single-lane road. - Correct arithmetic with units, plus a sanity check using a second method or everyday experience. - A practical recommendation, including a safety margin and how real signals would handle a queue this long. ### Follow-up Questions - How would the estimate change if some of the vehicles in the queue were trucks or buses? - Suppose the goal is to empty the queue while new cars keep arriving during the green. How would you work out the green time, and when could the queue never be cleared? - How would you check your estimate against what actually happens at a real intersection?