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21 people per minute enter a previously empty train station

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21 people per minute enter a previously empty train station [#permalink] New post 26 Aug 2017, 01:36
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21 people per minute enter a previously empty train station beginning at 7:00:00pm (7 o’clock and zero seconds). Every 9 minutes beginning at 7:04:00pm, a train departs and everyone who has entered the station in the last 9 minutes gets on the departing train. If the last train departs at 8:25:00, what is the average number of people who get on each of the trains leaving from 7:00:00 to 8:25:00, inclusive?

(A) 84
(B) 136.5
(C) 178.5
(D) 189
(E) 198.5
[Reveal] Spoiler: OA

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Re: 21 people per minute enter a previously empty train station [#permalink] New post 05 Oct 2017, 18:06
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From 7pm to 7:04, 84 people enter the station (21 per minute). These 84 people will get on the 7:04 train.
After that, for each 9 minute period, 9(21) = 189 people will enter the station and then get on a train. These trains will leave at 7:13, 7:22, 7:31, 7:40, 7:49, 7:58, 8:07, 8:16, and 8:25.
Since 9 trains each have 189 people and the first train has 84 people, the average is: (9*189 + 1*84)/10 = 178.5

Thus the correct option is C.

Hope this helps
Re: 21 people per minute enter a previously empty train station   [#permalink] 05 Oct 2017, 18:06
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21 people per minute enter a previously empty train station

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