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Bessie the cow is competing in a cross-country skiing event at the winter Moolympic games. She starts out at a speed of 1 meter per second. However, as she becomes more tired over time, she begins to slow down. Each time Bessie slows down, her speed decreases: she moves at 1/2 meter per second after slowing down once, then 1/3 meter per second after slowing down twice, and so on.
You are told when and where Bessie slows down, in terms of a series of events. An event like this:
means that Bessie slows down at a specific time -- here, 17 seconds into the race. An event like this:
means that Bessie slows down at a specific distance from the start -- in this case, 10 meters.
Given a list of N such events (1 <= N <= 10,000), please compute the amount of time, in seconds, for Bessie to travel an entire kilometer. Round your answer to the nearest integer second (0.5 rounds up to 1).
2 T 30 D 10
Bessie slows down at time t = 30 and at distance d = 10.
Bessie travels the first 10 meters at 1 meter/second, taking 10 seconds. She then slows down to 1/2 meter/second, taking 20 seconds to travel the next 10 meters. She then reaches the 30 second mark, where she slows down again to 1/3 meter/second. The remaining 980 meters therefore take her 980 * 3 = 2940 seconds. The total time is therefore 10 + 20 + 2940 = 2970.