In and out of a train.
people per minute enter a previously empty train station beginning at pm. Every minutes beginning at pm, a train departs and everyone who has entered the station in the last minutes gets on the departing train. If the last train departs at pm, what is the average number of people who get on each of the trains leaving from pm to pm, inclusive?
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1 solution
From 7 till 7 : 0 4 we have 2 1 × 4 = 8 4 people.
Every 9 minutes gives 9 × 2 1 = 1 8 9 people.
From 7 : 0 4 − 8 : 2 5 we have 9 nine minutes intervals:
7 : 0 4 , 7 : 1 3 , 7 : 2 1 , 7 : 3 0 , 7 : 3 9 , 7 : 4 8 , 8 : 0 7 , 7 : 1 6 , 8 : 2 5 ⟹
The average is 1 + 9 1 ( 8 4 ) + 9 ( 1 8 9 ) = 1 7 8 . 5