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that hill,tl;dr

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24

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    #32
    im invisible
    Closed Accounts Posts: 4,372 ✭✭✭im invisible


    Kevin Duffy wrote: »
    That's not an answer. If they repeated it again the following day it would be possible for them to pass at a different place unless pace was exactly the same on both occasions.
    yeah, but the question is
    Is there a place where you were at the the same place at the same time on both days?
    i'd read that as 'any place', seeing as he is only doing it once (up and down), and if he were to do it again, there would be a specific (probably different) place on that occasion aswell


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    #33
    Doyler92
    Registered Users Posts: 2,664 ✭✭✭Doyler92


    Pherekydes wrote: »
    He starts down at 8 am on the second day.



    Certainly. Imagine he has a brother. One starts up at 8 am and one starts down at 8 am. No matter what speed they each do they must pass each other. At that moment they are at the same place at the same time.


    What if he has a sister?


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    #34
    Kevin Duffy
    Closed Accounts Posts: 3,439 ✭✭✭Kevin Duffy


    im invisible wrote: »
    yeah, but the question is
    i'd read that as 'any place', seeing as he is only doing it once (up and down), and if he were to do it again, there would be a specific (probably different) place on that occasion aswell

    Eh, what? It has to be the same place, at the same time, so a different place would mean the answer was "no".


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    #35
    looksee
    Registered Users Posts: 28,466 ✭✭✭✭looksee


    Ahem. Excuse me guys, I've already got it. Its not that complicated. :pac:


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    #36
    Doyler92
    Registered Users Posts: 2,664 ✭✭✭Doyler92


    looksee wrote: »
    Ahem. Excuse me guys, I've already got it. Its not that complicated. :pac:


    Care to enlighten us?


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    #37
    looksee
    Registered Users Posts: 28,466 ✭✭✭✭looksee


    Doyler92 wrote: »
    Care to enlighten us?

    see post 15


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    #38
    im invisible
    Closed Accounts Posts: 4,372 ✭✭✭im invisible


    ahhhhhhhh..........

    tl;dbw

    too long; didnt bother writing


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    #39
    davetherave
    Registered Users Posts: 3,379 ✭✭✭davetherave


    Day 1: Leaves at 0800 and reaches summit at 2000
    Day 2: Leaves at 0800 and reaches ground at 2000

    It could well be that the eight o'clock on the second day is referring to 2000 in which case the person would be at the summit at 2000hrs on both days. However if it refers to 0800 then it is near impossible to calculate without a rate of speed or what "sometimes running ,some times walking" is.
    Imagine the hill is 30 miles high. (That's some hill btw)

    The person could have run for 8 hours at a constant speed of 3 miles p/hour. He would have gotten to the 24 mile marker at 1600 hrs.

    Now coming back down if he walk for 8 hours at a constant speed of 0.75 miles p/hour then again they would have reached the 24 mile mark again at 1600 hours meaning they are at the same point at the same time on both days.


    But you have all just wasted time reading this because we don't know what speed or distance the man covered making this whole thing kind of pointless....


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    #40
    biko
    Registered Users Posts: 81,220 ✭✭✭✭biko


    At what time did the train leave the station again?


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    #41
    Ah nuts
    Registered Users Posts: 90 ✭✭Ah nuts


    The answer is yes.

    Speed intervals make no difference. It's basically the same as one person leaving the top of the hill in the morning and another leaving the bottom at the same time. Given that in takes both same time to travel they are going to meet somewhere on the route. Thus being in the same point at the same time.


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    #42
    im invisible
    Closed Accounts Posts: 4,372 ✭✭✭im invisible


    looksee wrote: »
    Ahem. Excuse me guys, I've already got it. Its not that complicated. :pac:
    but, but BUT...
    Pherekydes wrote: »
    He starts down at 8 am on the second day.



    Imagine he has a brother. One starts up at 8 am and one starts down at 8 am. No matter what speed they each do they must pass each other. At that moment they are at the same place at the same time.
    or imagine the hill as a 1 lap race in mariocart time trial whatever, do one lap, save your 'ghost' start another lap, and see your ghost start off up the hill, but do a 180 at the start, (you have put yourself at the 'top' of the hill) and go the wrong way around the track, , at some point you will meet your ghost at whatever time, in the same place of the track, the same amount of time since setting out


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    #43
    Kevin Duffy
    Closed Accounts Posts: 3,439 ✭✭✭Kevin Duffy


    Ah nuts wrote: »
    The answer is yes.

    Speed intervals make no difference. It's basically the same as one person leaving the top of the hill in the morning and another leaving the bottom at the same time. Given that in takes both same time to travel they are going to meet somewhere on the route. Thus being in the same point at the same time.

    The paces could vary all through the journey. If he reached the halway point going up at 1500 and the same point coming down at 1501, then all times would be different all the way and your solution would be invalid.


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    #44
    General General
    Registered Users Posts: 1,900 ✭✭✭General General


    Pherekydes wrote: »
    He starts down at 8 am on the second day.



    Certainly. Imagine he has a brother. One starts up at 8 am and one starts down at 8 am. No matter what speed they each do they must pass each other. At that moment they are at the same place at the same time.
    im invisible wrote: »

    or imagine the hill as a 1 lap race in mariocart time trial whatever, do one lap, save your 'ghost' start another lap, and see your ghost start off up the hill, but do a 180 at the start, (you have put yourself at the 'top' of the hill) and go the wrong way around the track, , at some point you will meet your ghost at whatever time, in the same place of the track, the same amount of time since setting out

    Yo. You guys be trying to teach some pigs how to sing.


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    #45
    westendgirlie
    Closed Accounts Posts: 2,125 ✭✭✭westendgirlie


    where do i go from here wrote: »
    Between 8pm and 8am you're at the top i.e on both days.



    First serious answer i ever gave on here:rolleyes:

    That's what I said!

    Anyone else think this "hill" would be the ideal place to meet for boards beers?


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    #46
    theboss80
    Registered Users Posts: 1,838 ✭✭✭theboss80


    The bottom of the hill

    /thread


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    #47
    OutlawPete
    Closed Accounts Posts: 17,689 ✭✭✭✭OutlawPete


    housetypeb wrote: »
    Is there a place where you were at the the same place at the same time on both days?

    Yes, Planet Earth.


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    #48
    Pherekydes
    Registered Users Posts: 16,164 ✭✭✭✭Pherekydes


    Kevin Duffy wrote: »
    The paces could vary all through the journey. If he reached the halway point going up at 1500 and the same point coming down at 1501, then all times would be different all the way and your solution would be invalid.

    The solution is so simple you are not seeing it. If they leave at the same time then speed is irrelevant. They must pass each other at some point. That is the point at which they are at the same point at the same time.

    Use the example I gave earlier of the brother (sister, ghost, alter ego, whatever).


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    #49
    Pherekydes
    Registered Users Posts: 16,164 ✭✭✭✭Pherekydes


    where do i go from here wrote: »
    Between 8pm and 8am you're at the top i.e on both days.

    Unfortunately, the original question asked:
    at the the same place at the same time on both days?

    It must be at the same time! The period of time you gave is from 8pm to 8 am. i.e. every period on the first day is different from every period on the second day.

    First day: 2000-2359
    Second day: 0000-0800


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    #50
    animan
    Registered Users Posts: 510 ✭✭✭animan


    I think this is one for the grand old duke of york :)


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    #51
    Jazzy
    Banned (with Prison Access) Posts: 6,315 ✭✭✭Jazzy


    https://www.youtube.com/watch?v=wp43OdtAAkM


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    #52
    pebbles21
    Registered Users Posts: 1,817 ✭✭✭pebbles21


    animan wrote: »
    I think this is one for the grand old duke of york :)

    Or Jack and Jill ;)


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    #53
    Little Acorn
    Registered Users Posts: 1,531 ✭✭✭Little Acorn


    OutlawPete wrote: »
    Yes, Planet Earth.

    Exactly what I was thinking.
    He didn't ask "at the the same place on the hill at the same time on both days?
    Due to wording, I believe Planet Earth should also be an accepted answer.:)


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    #54
    ocallagh
    Registered Users Posts: 3,140 ✭✭✭ocallagh


    Pherekydes wrote: »
    The solution is so simple you are not seeing it. If they leave at the same time then speed is irrelevant. They must pass each other at some point. That is the point at which they are at the same point at the same time.

    Use the example I gave earlier of the brother (sister, ghost, alter ego, whatever).

    This is incorrect. If you replace the bolded bit with
    They must pass each other at some point. That is the point at which they are at the same point.
    it makes sense, but then it's not really proving anything.

    If they travel at a constant speed then yes they will be at the same place at the same time (providing the place and time doen't have to be accurate to nano metres/seconds or something), but if their speed varies (as per op's description) they will not necessarily be in the same place at the same time.


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    #55
    chicken fingers
    Closed Accounts Posts: 645 ✭✭✭chicken fingers


    something something north pole, OP does not have a talent for communication.


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    #56
    mackg
    Registered Users Posts: 3,938 ✭✭✭mackg


    ocallagh wrote: »
    This is incorrect. If you replace the bolded bit with it makes sense, but then it's not really proving anything.

    If they travel at a constant speed then yes they will be at the same place at the same time (providing the place and time doen't have to be accurate to nano metres/seconds or something), but if their speed varies (as per op's description) they will not necessarily be in the same place at the same time.

    The question is simply is there a point where they pass each other, which is what was proven in the post you are referring to. Where the point they pass each other is and what time they pass each other at is irrelevant.


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    #57
    Kevin Duffy
    Closed Accounts Posts: 3,439 ✭✭✭Kevin Duffy


    Pherekydes wrote: »
    The solution is so simple you are not seeing it. If they leave at the same time then speed is irrelevant. They must pass each other at some point. That is the point at which they are at the same point at the same time.

    Use the example I gave earlier of the brother (sister, ghost, alter ego, whatever).

    You're taking the two-brothers attempt to illustrate as though it becomes a fact - it doesn't, there is only one person on the hill at a time. To further use your illustration - if you don't know the respective paces, you couldn't predict when and where the brothers would meet as you can't say where they'd be on the hill at any given time. Without knowning speed up and down in the single person scenario you can't know it's recreated the following day, so there is no way to say if there is a point at which you are at the same place at the same time.


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    #58
    Pherekydes
    Registered Users Posts: 16,164 ✭✭✭✭Pherekydes


    Kevin Duffy wrote: »
    You're taking the two-brothers attempt to illustrate as though it becomes a fact - it doesn't...

    No, I'm not. It's just an aid to help visualise the solution.

    The original question asks, "Is there a point where he is at the same point at the same time of day?" The prerequisites are: he starts up at 8am the first day, and starts down at 8am the second day. It takes him the same time each day [12 hrs].

    Now, to visualise what's going on, imagine there are two people. One starts up at 8am and one starts down at 8am, on the same day. They must pass each other.

    Speed is irrelevant. If you don't see it now there's nothing else I can say.

    Incidentally, I've seen this problem before, in college. That is the correct solution, and that is the way to visualise it.


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    #59
    Kevin Duffy
    Closed Accounts Posts: 3,439 ✭✭✭Kevin Duffy


    Pherekydes wrote: »
    No, I'm not. It's just an aid to help visualise the solution.

    The original question asks, "Is there a point where he is at the same point at the same time of day?" The prerequisites are: he starts up at 8am the first day, and starts down at 8am the second day. It takes him the same time each day [12 hrs].

    Now, to visualise what's going on, imagine there are two people. One starts up at 8am and one starts down at 8am, on the same day. They must pass each other.

    Speed is irrelevant. If you don't see it now there's nothing else I can say.

    Incidentally, I've seen this problem before, in college. That is the correct solution, and that is the way to visualise it.

    Well, that solution was wrong in college and it's wrong again now. Just 'cos you saw it there and accepted it doesn't make it right and to be frank "I saw it in college" is not a solution to anything. If there were two people, of course they would pass each other, but there aren't, so that illustration is irrelevant.
    Supposing you take your illustration and they do it twice, over 4 days - without known speeds, it's possible they'll pass each other at different places each time. Same in the single person scenario, without known speeds, he could do that journey differently every time, no matter how many times he took it.


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    #60
    mackg
    Registered Users Posts: 3,938 ✭✭✭mackg


    housetypeb wrote: »
    One day,starting at Eight o clock,you go up a hill ,sometimes running and sometimes walking and it takes 12 hours, you spend the night on the hill top.
    Next day,starting at Eight o clock, you start back down, sometimes running ,some times walking and it takes 12 hour again
    Is there a place where you were at the the same place at the same time on both days?

    When they travel at varying speeds of course there is no way to tell where they would meet but that isn't the question. The brothers method does however answer the question in the OP


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    #61
    pickarooney
    Moderators, Arts Moderators Posts: 35,462 Mod ✭✭✭✭pickarooney


    Kevin Duffy wrote: »
    The paces could vary all through the journey. If he reached the halway point going up at 1500 and the same point coming down at 1501, then all times would be different all the way and your solution would be invalid.

    But the half-way point is only a single example of an infinite number of possible meeting points and times. In this case, the actual meeting point would be something like a few metres higher up and at 15.00.30

    If you don't accept the two brothers example as an easy way to illustrate the answer, make it harder - Draw (or visualise) a red line going up the hill, marking each second spent climbing, then do the same with a green line coming down. They'll meet somewhere. This is just an example of one pair of speeds travelling. The meeting point can be shunted up or down the line according to how fast each one travels.

    The mistake to avoid in this is to consider the speeds and the time since starting as important for each leg of the journey. They're irrelevant, just included to confuse you.


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