Page 2 of 3 FirstFirst 123 LastLast
Results 16 to 30 of 34

Math Help - Motorcycle and Walking Rates and Times

  1. #16
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,102
    Thanks
    67

    Re: Motorcycle and Walking Rates and Times

    Quote Originally Posted by godelproof View Post
    > No need for that! Solution to the problem exists as long as M>C...
    Ya...really then, all it is a "2 walker" solution, with 3rd walker made to fit in:
    L / (time-for-2-walkers) .

    >EDIT: Did your program search for cases where M may carry a person backwards?
    No.
    Last edited by Ackbeet; June 16th 2011 at 06:27 PM. Reason: Split out Wilmer's comments.
    Follow Math Help Forum on Facebook and Google+

  2. #17
    Member
    Joined
    May 2009
    Posts
    146

    Re: Motorcycle and Walking Rates and Times

    Quote Originally Posted by Wilmer View Post
    >EDIT: Did your program search for cases where M may carry a person backwards?

    No.
    see the example in #9. there you must carry B backwards. I suspect even in this case my formular gives correct answer... are you able to modify your program to include this cases, too? If so, can you still "see" my fomular "fits" perfectly what your modified program does?
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Member
    Joined
    May 2009
    Posts
    146

    Re: Motorcycle and Walking Rates and Times

    Quote Originally Posted by Wilmer View Post
    No need for that! Solution to the problem exists as long as M>C...

    Ya...really then, all it is a "2 walker" solution, with 3rd walker made to fit in:
    L / (time-for-2-walkers) .
    Sorry for my claim. It is wrong...
    Consider L=1000, A=1, B=999, C=1000, M=1001. Here M>C but unfortunely there's no feasible plan.

    Quote Originally Posted by Wilmer View Post
    Lots of math superstars at this site (does not include me!), and find it sort of strange
    nobody else has responded...since I find this a very interesting "puzzle".
    Me, too! I didn't expect the general problem to turn out to be so complicated. Why nobody responses? I guess most people just browse the first few posts of the thread and think it's just a matter of computation of a specific problem? Anyway this thread is getting too long... Perhaps it's better to post the generalised problem to some other subforum?
    Last edited by godelproof; June 17th 2011 at 10:52 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #19
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    909
    Thanks
    27

    Re: Motorcycle and Walking Rates and Times

    Hello.
    I have followed this post from the beginning.I made calculations to see if I could estimate the time for the walkers to reach the other end.My inital estimate was 4 hours I started by sending M to pick up the slowest walker and to drop him at a point where the time to do the same for the others would keep him from crossing the finish line.Rate of walkers .1 K per minute,.133, .166. Rate of M 2K per minute.It takes M to meet a 57 minutes.They approach each other at 2.1 K per minute. The trip back to the 90 mile mark takes 47 minute. The pick up point was at mile 5.7. Picking up the others took a total of 247 minutes. I can see that the drop offs should have been closer to the end.Final back and forth movements ofM to get walkers in correct positions would take little time.





    bjh
    Follow Math Help Forum on Facebook and Google+

  5. #20
    Member
    Joined
    May 2009
    Posts
    146

    Re: Motorcycle and Walking Rates and Times

    Quote Originally Posted by godelproof View Post
    Two questions:

    1) Given any configuration ({a}_{1},{a}_{2},...,{a}_{n},m,L), if a feasible plan exists, so does a feasible plan that takes least time {T}_{least} . Is {T}_{least} always equal to {T}_{min} in #10, upon substituting ({a}_{1},{a}_{2},...,{a}_{n},m,L)?

    2) Given any configuration ({a}_{1},{a}_{2},...,{a}_{n},m,L), how can we decide if a feasible plan exists at all?
    Now to the first question, the answer is NO! See #21 and #22.

    To the second question: Go here http://www.mathhelpforum.com/math-he...tml#post660726
    Last edited by godelproof; June 18th 2011 at 06:26 AM.
    Follow Math Help Forum on Facebook and Google+

  6. #21
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,102
    Thanks
    67

    Re: Motorcycle and Walking Rates and Times

    Integer example (2 walkers) where 1 walker is driven backward.

    L = 1080 (X to Y), M = 100, A = 20, B = 80

    M and B meet after 6 hours.
    M drives B backward for 2 hours.
    B then walks to Y : 10 hours ; total = 18 hours

    After the 1st 8 hours, A has walked 160.
    M is now 120 from A: takes 1 hour to meet A.
    Distance from Y now 900: takes 9 hours ; total = 18 hours.
    Follow Math Help Forum on Facebook and Google+

  7. #22
    Member
    Joined
    May 2009
    Posts
    146

    Re: Motorcycle and Walking Rates and Times

    Quote Originally Posted by Wilmer View Post
    Integer example (2 walkers) where 1 walker is driven backward.

    L = 1080 (X to Y), M = 100, A = 20, B = 80

    M and B meet after 6 hours.
    M drives B backward for 2 hours.
    B then walks to Y : 10 hours ; total = 18 hours

    After the 1st 8 hours, A has walked 160.
    M is now 120 from A: takes 1 hour to meet A.
    Distance from Y now 900: takes 9 hours ; total = 18 hours.
    Nice. And my formular gives: (1080/20+1080/80)/(1/2+20/80+80/20)=270/19 \approx14.21, which is obviously impossible.
    Follow Math Help Forum on Facebook and Google+

  8. #23
    Member
    Joined
    May 2009
    Posts
    146

    Re: Motorcycle and Walking Rates and Times

    Quote Originally Posted by bjhopper View Post
    Hello.
    I have followed this post from the beginning.I made calculations to see if I could estimate the time for the walkers to reach the other end.My inital estimate was 4 hours I started by sending M to pick up the slowest walker and to drop him at a point where the time to do the same for the others would keep him from crossing the finish line.Rate of walkers .1 K per minute,.133, .166. Rate of M 2K per minute.It takes M to meet a 57 minutes.They approach each other at 2.1 K per minute. The trip back to the 90 mile mark takes 47 minute. The pick up point was at mile 5.7. Picking up the others took a total of 247 minutes. I can see that the drop offs should have been closer to the end.Final back and forth movements ofM to get walkers in correct positions would take little time.





    bjh
    Thanks~ So how can this example further help us?
    Follow Math Help Forum on Facebook and Google+

  9. #24
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    909
    Thanks
    27

    Re: Motorcycle and Walking Rates and Times

    godelproof you didn't answer my question.



    bjh
    Follow Math Help Forum on Facebook and Google+

  10. #25
    Member
    Joined
    May 2009
    Posts
    146

    Re: Motorcycle and Walking Rates and Times

    Quote Originally Posted by bjhopper View Post
    godelproof you didn't answer my question.



    bjh
    what is your question?
    Follow Math Help Forum on Facebook and Google+

  11. #26
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,102
    Thanks
    67

    Re: Motorcycle and Walking Rates and Times

    Quote Originally Posted by godelproof View Post
    ....it may exist even if M<C. But that's contingent.
    Huh? If Motorcycle speed < fastest walker speed, then ONLY possible case is
    to have ALL walkers at fastest walker speed, and the Motorcycle is useless.
    That's the only way to reach destination at same time. Agree?

    Remark on case where a walker is driven backward:
    it is possible to get a solution where a walker is driven back BEHIND (West of) starting point X.
    The wording of your problem does not prevent that.
    Follow Math Help Forum on Facebook and Google+

  12. #27
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    909
    Thanks
    27

    Re: Motorcycle and Walking Rates and Times

    My question. How many hours have you estimated are required to complete the task. Just give your numbers without lengthy comments.Thanks.



    bjh
    Follow Math Help Forum on Facebook and Google+

  13. #28
    Member
    Joined
    May 2009
    Posts
    146

    Re: Motorcycle and Walking Rates and Times

    a1=.1 a2=.133 a3=.166 m=2
    What is L? L=2.1*57=1197/10?
    Follow Math Help Forum on Facebook and Google+

  14. #29
    Member
    Joined
    May 2009
    Posts
    146

    Re: Motorcycle and Walking Rates and Times

    Quote Originally Posted by Wilmer View Post
    Huh? If Motorcycle speed < fastest walker speed, then ONLY possible case is
    to have ALL walkers at fastest walker speed, and the Motorcycle is useless.
    That's the only way to reach destination at same time. Agree?
    I don't agree
    Say a=100, b=99, c=98 and m=99.9, L=100
    what do you say? m first meets a and drive him back to somewhere between b and c, then pick up c to make everybody arrive the same time at destination. Calculations should be similar to that done here http://www.mathhelpforum.com/math-he...tml#post660891 and a feasible plan exists.
    Follow Math Help Forum on Facebook and Google+

  15. #30
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,102
    Thanks
    67

    Re: Motorcycle and Walking Rates and Times

    Quote Originally Posted by godelproof View Post
    Say a=100, b=99, c=98 and m=99.9, L=100
    m first meets a and drive him back to somewhere between b and c, then pick up c to make everybody arrive the same time at destination.
    After M drives A back, M then drops A off, then M goes forward to pick up C.
    But A will also go forward : both leave together going forward, and M will never
    be able to catch up, since speed slower....
    Follow Math Help Forum on Facebook and Google+

Page 2 of 3 FirstFirst 123 LastLast

Similar Math Help Forum Discussions

  1. walking speed
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 2nd 2010, 01:10 PM
  2. Walking to Work
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 2nd 2010, 10:31 PM
  3. Walking robots
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: June 22nd 2009, 10:32 PM
  4. Walking Up a Hill
    Posted in the Geometry Forum
    Replies: 7
    Last Post: March 3rd 2008, 12:03 PM
  5. Walking Rates
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 14th 2008, 08:42 PM

Search Tags


/mathhelpforum @mathhelpforum