CTK Exchange
Front Page
Movie shortcuts
Personal info
Awards
Reciprocal links
Terms of use
Privacy Policy

Interactive Activities

Cut The Knot!
MSET99 Talk
Games & Puzzles
Arithmetic/Algebra
Geometry
Probability
Eye Opener
Analog Gadgets
Inventor's Paradox
Did you know?...
Proofs
Math as Language
Things Impossible
My Logo
Math Poll
Other Math sit's
Guest book
News sit's

Recommend this site

Manifesto: what CTK is about |Store| Search CTK Buying a book is a commitment to learning Table of content Things you can find on CTK Chronology of updates Email to Cut The Knot Recommend this page

CTK Exchange

Subject: "Optimization mod problem"     Previous Topic | Next Topic
Printer-friendly copy     Email this topic to a friend    
Conferences The CTK Exchange College math Topic #410
Reading Topic #410
nbro0
Member since Jan-2-04
Jan-02-04, 05:14 PM (EST)
Click to EMail nbro0 Click to send private message to nbro0 Click to view user profileClick to add this user to your buddy list  
"Optimization mod problem"
 
   Folks,

I came across this problem studying for GRE. Seems like a possibility for a mod-based solution.

An airline passenger is planning a trip that involves 3 connecting flights that leave from airport A, B, C. The first flight leaves the airport A starting at 8:00am and arrives at Airport B, 2 1/2 hrs later. The second flight leaves Airport B every 20 mins beginning at 8:00am, and arrives at airport C 1 1/6 hours later. The third flight leaves airport C every hour, beginning at 8:45 am. What is the least amount of time that the passenger can spend between flights to keep their connections?

I was able the brute force the correct answer (65 mins). However couldn't help shake the fact that there might be a more general, elegant modulo solution. Any takers?


  Alert | IP Printer-friendly page | Reply | Reply With Quote | Top
mptack
Member since Nov-24-04
Nov-24-04, 11:05 AM (EST)
Click to EMail mptack Click to send private message to mptack Click to view user profileClick to add this user to your buddy list  
1. "RE: Optimization mod problem"
In response to message #0
 
  
I was also able to brute force the solution with the help of a spreadsheet.

Have you tried converting flight times into minutes and then trying mod(flighttime,time between flights)?

At the end you'll have to add another 15 mins because the flights from the last airport leave hourly beginning at 8:45 rather than on the half hour.

If the flights from the airport C left every 20min beginning at 8:30 or even 9:30 waiting time would have been 50min. Which I arrive at via a couple of modulo functions.

Try it first. If you can't get it. Post another e-mail.


  Alert | IP Printer-friendly page | Reply | Reply With Quote | Top
Graham C
Member since Feb-5-03
Nov-24-04, 05:50 PM (EST)
Click to EMail Graham%20C Click to send private message to Graham%20C Click to view user profileClick to add this user to your buddy list  
2. "RE: Optimization mod problem"
In response to message #0
 
   >
>An airline passenger is planning a trip that involves 3
>connecting flights that leave from airport A, B, C. The
>first flight leaves the airport A starting at 8:00am and
>arrives at Airport B, 2 1/2 hrs later. The second flight
>leaves Airport B every 20 mins beginning at 8:00am, and
>arrives at airport C 1 1/6 hours later. The third flight
>leaves airport C every hour, beginning at 8:45 am. What is
>the least amount of time that the passenger can spend
>between flights to keep their connections?
>

Am I missing something here? There should be a choice of flights from A perhaps?

For every extra 20 minutes he waits at B (in the first hour) he cuts his waiting time at C by 20 minutes. Makes no difference therefore which flight he takes.

Timetable

.......B................C
.arr.......dep.......arr.......dep.......wait
10:30.....10:40.....11:50.....12:45......10 plus 55 = 65
..........11:00.....12:10.....12:45......30 plus 35 = 65
..........11:20.....12:30.....12:45......50 plus 15 = 65

Briefly he has to arrive at B at 10:30 and has to leave C at 12:45 at the earliest, which is 2:15 in all. He spends 1:10 on the plane, so he has to wait 1:05 minutes.


  Alert | IP Printer-friendly page | Reply | Reply With Quote | Top

Conferences | Forums | Topics | Previous Topic | Next Topic

You may be curious to have a look at the old CTK Exchange archive.
Please do not post there.

|Front page| |Contents|

Copyright © 1996-2018 Alexander Bogomolny

66167581

Search:
Keywords:

Google
Web CTK