# Got a Math question

Discussion in 'Community Discussion' started by calyxman, Oct 29, 2006.

1. ### calyxman macrumors 6502a

Joined:
Apr 17, 2005
#1
While tutoring at the local community college, I ran into a word problem today that I found rather interesting. Here's the question (and I'm paraphrasing the problem to the best of my ability):

Just would like to know the methodology you would use to solve this. Thanks!

2. ### Mr. Anderson Moderator emeritus

Joined:
Nov 1, 2001
Location:
VA
#2
what's the initial state? Empty station or full - its kind of important.

D

3. ### swiftaw macrumors 603

Joined:
Jan 31, 2005
Location:
Omaha, NE, USA
#3
Ok, since it doesn't mention how often trains depart, let us just assume continual departures that would empty a full station in 40 minutes. Also, assume station is initially empty.

Thus, the amount of people who have entered the station by time t (as a percentage of the station capacity) is 100t/30 [Check that at time t=30, the station is 100% full, as described]

Similarly, the amount of people who have left the station on trains by time t (as a percentage of the station capacity) is 100t/40 [Check that at t=40, 100% of the capacity has been removed, as described]

Thus, at time t, the amount of people left in the station (as a percentage of total capacity) is 100t/30 - 100t/40 [People in - people out]

When does the station get full? whenever the above = 100%

thus, solving 100t/30 - 100t/40 = 100

implies that 4t - 3t = 120

Thus t =120 minutes = 2hours

### Staff Member

Joined:
Jan 20, 2005
#4
If I understand the question correctly (and assuming you start from an empty station), here's how I look at it. (It also includes some assumptions about the rates of ingress and egress remaining constant, which isn't entirely valid, especially in the egress rate.)

Say the capacity of the station is x. In 30 minutes, x people will enter the station. But it take 40 minutes for x people to exit the station, so .75x people exit in 30 minutes. So after 30 minutes, x people have come in and .75x people have left, leaving the station with .25x people inside.

After an hour, you have a total of 2x people having entered, with 1.5x people having left, giving .5x left in the station after an hour. Continuing with this train (pun entirely intended) of thought, the station would be full after 2 hours.

Joined:
Aug 14, 2006
Location:
London, UK
6. ### swiftaw macrumors 603

Joined:
Jan 31, 2005
Location:
Omaha, NE, USA
#6
Seems like we understood the question in the same way

7. ### Chundles macrumors G4

Joined:
Jul 4, 2005
#7
OK, there are some assumptions you have to make:

1. The station would be full in 30 minutes.
2. The first train will be 10 minutes late but because the government changed the leeway on arrival times it still counts as "on time."
3. If the trains are now all late, they will get progressively later.
4. The train broke down on a day when a sporting event was occurring.

So, seeing as all four of those are correct, the train station will in fact fill up in 15 minutes and won't be empty until 4:55pm - the train arriving at 4:55pm actually being the one due to arrive at 3:42pm but seeing as how there is actually a train due at 4:55pm (although that train won't arrive till 6:35pm) everything is now considered "on time."

8. ### calyxman thread starter macrumors 6502a

Joined:
Apr 17, 2005
#8
Cool, so I got the same answer. By the way, the assumption is that the station starts off empty.

The method I used was the following: 1/30 - 1/40 = 1/x

9. ### swiftaw macrumors 603

Joined:
Jan 31, 2005
Location:
Omaha, NE, USA
#9
Hmm, seems like you have managed to get hold of a copy of British Rail's secret operating handbook

10. ### Fearless Leader macrumors 68020

Joined:
Mar 21, 2006
Location:
Hoosiertown
#10
very nice

so anywhere from-30 mins to 2 hours...

11. ### calyxman thread starter macrumors 6502a

Joined:
Apr 17, 2005
#11
LOL. I bet you were the one who wrote the answer to this question:

12. ### swiftaw macrumors 603

Joined:
Jan 31, 2005
Location:
Omaha, NE, USA
#12
Haha, too funny. If I were grading that I would have given that kid credit, just for making me laugh

13. ### Chundles macrumors G4

Joined:
Jul 4, 2005
#13
So, BR is making it secret eh? It's very much out in the open here.

14. ### Fearless Leader macrumors 68020

Joined:
Mar 21, 2006
Location:
Hoosiertown
#14
almost as good as:
separate.
2(5x+8)
2 ( 5 x + 8 )