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TSA 2014 · Question 18 · Optimisation

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A main road crosses a side road and the junction is controlled by a set of traffic lights. The normal sequence is for the lights to be green for 25 seconds on the main road followed by 15 seconds of green for the side road. There is also a pedestrian phase in the lights when all the road lights are red. If a pedestrian presses a button to cross any of the roads then, after the side road lights have been green, the pedestrian lights turn green for 10 seconds. Following a pedestrian phase, the main road green period is increased to 35 seconds to clear the build-up. Whenever any of the lights change there is a two-second period when all lights are red. The time on amber is included in the green times given above.

What is the longest time traffic on the side road will have to wait for their lights to go green?