How long will you keep the traffic light green in order to allow 100 cars to pass through? (Assume a single lane road)

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Asked at Revolut over a year ago

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SR · Answer 1 · 2022-01-03T20:12:50+0000

Assumptions

Single lane road
Speed limit on road - 20 m/hr
Avg length of car 3 m
Distance between cars - 3 m (1 car lengths) (assme all cars are standstill when the lights turn to green)
Other things like - good visibility; no acc and all that

Calculations

Total distance to be covered for first car = length of first car + space between cars = 3+ 3 = 6 m
Total distance to be covered for 100 cars = (Total distance to be covered for a car) * 100 - (space behind 100th car) = 6m * 100 - 3m = 597 m ~= 600m = 0.6 km = 0.36 miles
Time = Distance / Speed = 0.36 / 20 hours = 0.018 hours = 60 * 0.018 mins = 1.08 mins

Rafa · Answer 2 · 2021-12-26T19:46:52+0000

Clarification Questions

-What is the allowed speed? 100KM/h

Assumptions

-All of the vehicles are the same

-Length

-Acceleration

-No special condition

-The visibility is good

-Straight road

-All of the drivers are the same

-In good shape and feel good.

-Accelerate the same.

-Drive according to the law (no more than 100km/h) – w/o unexpected brakes.

-

The equations: Time until the last driver starts to drive + time it takes the last driver to pass the traffic light

Length of a car 4m, cars take 1m distance between each other -> 5 X 100 – 1 = 499m ~500m

It takes a car about 15 sec to reach max speed; during that time, I assume it passes ~150m

And for the other 350m it drives at the speed of 100km/h -> 10km in 6 min -> 1km in 36 sec ->~12 sec to pass the 350m.

In total, it will take the last vehicle 27 sec to pass the distance.

How long until the last vehicle starts?

As far as I remember, it takes ¾ sec for a person to react, +0.5 sec to start to move -> 1.25 sec to move so the driver behind will notice.

1.25 X 100 drivers -> 125 sec

The final result 125 sec + 27 sec = 152 sec -> 2.5 min.