Doug is interested in traveling to Brilliantia . From his house, he walked to the starting bus terminal, where there are two different buses both about to depart simultaneously. Before his travel, he went inside both buses to ask about the bus stops between his current location and the final stop. He learned that:
Which bus should he take in order to minimize the total time elapsed between the starting and ending terminals - local or limited buses?
Note: Neglect heavy traffic, crowds, detours and accidents throughout the trip.
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If you hand-solve for the first several minutes, you'll find a pattern that, for every k ≥ 3 , at T = 6 k − 3 , the local bus arrives at station 2 k and stay for 1 minute, and at T = 6 k − 2 , the local bus leaves while the limited bus arrives and stay for 2 minutes.
The following table serves as an induction.
Therefore, the local bus would arrive at station 35 two minutes earlier than the limited bus, as is shown in the table above.