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TSA Original Paper 1 · Question 43 · Optimisation

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A railway level crossing has barriers controlled by traffic lights. The normal sequence is for the road to have a green light for 40 seconds, followed by the barriers coming down for trains to pass. When a train approaches, the lights turn amber for 3 seconds, then red. The barriers take 8 seconds to fully lower. Trains take 25 seconds to pass through the crossing. After a train passes, the barriers take 8 seconds to rise. However, if a second train is detected while the first train is passing, the barriers remain down and there is a 15-second safety gap before the second train passes through. Whenever the lights change from green to red, or from red back to green, there is always the 3-second amber phase.

What is the longest time road traffic will have to wait at a red light if two trains pass through consecutively?