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  • Three runners : Do they ever meet??

    freak16

    freak16

    @freak16-XgiLj6
    Updated: Oct 21, 2024
    Views: 1.2K
    In a circular race track of length 100 m, three persons A, B and C start together. A
    and B start in the same direction at speeds of 10 m/s and 8 m/s respectively. While C
    runs in the opposite at 15 m/s. When will all the three meet for the first time on the after
    the start?

    a) After 4 s
    b) After 50 s
    c) After 100 s
    d) After 200 s

    Plz solve it...
    0
    Replies
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Replies

  • YOUNGGRASSHOPPER

    Member • Dec 27, 2010

    I will go with a.
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  • Sachin Jain

    Member • Dec 27, 2010

    @ Young Grass Hopper
    Can you please explain your approach.
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  • Saandeep Sreerambatla

    Member • Dec 27, 2010

    They will meet after 100 sec.
    by back substitution I have solved this.

    According to the options, if we go for b. Then A travels 500m , and b 400m and C - 750m. A and B are at the start point but not C.

    So after 100 sec they will meet.
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  • freak16

    Member • Dec 27, 2010

    Can u plz explain your approach??
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  • Sachin Jain

    Member • Dec 27, 2010

    @ freak16
    I got English scared is trying to say.
    I think he used options and tried to satisfy which option suited best.
    Firstly create an image of race track in your mind. That is it is circular and 100 m in length
    A,B,C are at starting points but run in different directions with different speeds.
    This is the scenario.

    Now take Option (a) 4s
    A-> 40m
    B-> 32m
    c-> 60m
    That means A and C meet in this case but B does not.
    So this option is wrong

    Now take Option B
    A->500
    B->400
    c->750

    A and B come back at the starting points but C is in half way of track.
    So this is also wrong

    This way go on and you will get the answer.
    I hope i am clear....
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  • freak16

    Member • Dec 27, 2010

    @Es
    You rock!!
    can u plz tell me their second meet will be after 200s and like that they will meet after every 100 sec..
    M i right??
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  • freak16

    Member • Dec 27, 2010

    @blunderboy
    plz reply to my above post..😀
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  • YOUNGGRASSHOPPER

    Member • Dec 27, 2010

    I took the 100m circle track and devided it in half. With A abnd B running one direction and C running in the opposing the total distance that has to be covered by group A B and group C is still 100m before they meet the first time.

    A) will travel 40m in 4s. 4s times 10m/s

    B) will travel 32m in 4s. 4s times 8m/s

    C) will travel 60m in 4s. 4s times 15m/s

    A and C will be the first to meet in 4s and B and C will still be 8m from first point of contact.

    That is why I chose Answer a) After 4s.
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  • Sachin Jain

    Member • Dec 27, 2010

    @freak16 Yes you are right....😀
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  • ChaZ-E

    Member • Oct 6, 2014

    A takes (100m) / (10m/s) = 10s to finish one complte round.
    B takes (100m) / (8m/s) = 12.5s to finish one complte round.
    C takes (100m) / (15m/s) = (20/3)s to finish one complte round.
    For them to meet, the time will be LCM of above three times ie LCM(10,12.5,20/3)
    = LCM(10/1,25/2,20/3)
    = LCM(60,75,40)/LCM(1,2,3)
    =600/6
    =100sec
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  • Shashank Moghe

    Member • Oct 6, 2014

    After 100 seconds, at the starting point.
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