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21 people per minute enter a previously empty train station

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Carcass
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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
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C
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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
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Re: 21 people per minute enter a previously empty train station [#permalink] New post   21 Aug 2019, 22:14
I get mixed up that they started counting the 9 min from 7.04 and didn't understand that a train came at 7.04. How did you get it ?
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21 people per minute enter a previously empty train station [#permalink] New post   22 Aug 2019, 06:37
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Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project




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


Time | # of people at station
7:00:00 | 0
7:01:00 | 21
7:02:00 | 42
7:03:00 | 63
7:04:00 | 84
7:04:00 train arrives and takes all 84 people

7:05:00 | 21
7:06:00 | 42
7:07:00 | 63
7:08:00 | 84
7:09:00 | 105
7:10:00 | 126
7:11:00 | 147
7:12:00 | 168
7:13:00 | 189
7:13:00 train arrives and takes all 189 people

We can extrapolate from here to just keep track of the number of passengers each train picks up.
We get:
7:13:00 train arrives and takes all 189 people
7:22:00 train arrives and takes all 189 people
7:31:00 train arrives and takes all 189 people
7:40:00 train arrives and takes all 189 people
7:49:00 train arrives and takes all 189 people
7:58:00 train arrives and takes all 189 people
8:07:00 train arrives and takes all 189 people
8:16:00 train arrives and takes all 189 people
8:25:00 train arrives and takes all 189 people

In total, 10 trains arrived and left
1 train took 84 people
9 trains took 189 people

Average = [(1)(84) + (9)(189)]/10
= [84 + 1701]/10
= 1785/10
= 178.5

Answer: C

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Re: 21 people per minute enter a previously empty train station [#permalink] New post   22 Aug 2019, 13:46
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Asmakan wrote:
I get mixed up that they started counting the 9 min from 7.04 and didn't understand that a train came at 7.04. How did you get it ?


Here's a way that I think is fast for doing the problem.

From 7-8:25 there are 60+25 minutes. So 85 minutes and 21 people arrives in each of those minutes.

While there are 85 minutes for people to arrive, trains start 4 minutes later giving them only 81 minutes to show up AFTER THE FIRST TRAIN. 1+ 81/9 = 1 + 9 = 10.

Finally (total people) /(total trains) = the answer which his 85*21/ 10 = 178.5

answer is C.
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21 people per minute enter a previously empty train station [#permalink] New post   20 Jun 2021, 00:35
From 7:00:01 pm to 7:04:01, 84 people enter the first train (21 per
minute). These 84 people will depart at 7:04.
After that, for each 9-minute period, 9(21) = 189 people will enter the next
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
Note that the strange time format (minutes and seconds) doesn’t make the
problem any harder—the problem is actually clearer because people board the
train at 1 second after each minute, whereas the train leaves at the beginning
of each minute.
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Re: 21 people per minute enter a previously empty train station [#permalink] New post   27 Dec 2022, 10:41
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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