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Math Help - towns

  1. #1
    Newbie
    Joined
    Aug 2005
    Posts
    8

    Help!!!!

    On a bus route between towns A and H, there are six other towns: B, C, D, E, F and G. Each segment of the route between two towns that passes through exactly two more towns is of length at least 23 km. Each segment of the route between two towns that passes through exactly one more town is of length at most 18 km. If the length of the whole route is 51 km, what are possible lengths of the segment of the route between D and E?
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    1,631
    Here is one way.

    ABCD is from 23km to 51km
    So, 23 <= ABCD <= 51 ----------(i)

    ABCDEFG = 51
    DEFG = ABCDEFG -ABCD
    So, DEFG is from 28km to 0km
    0 <= DEFG <= 28 ---------------(ii)

    EFG is from 18km to 0km,
    0 <= EFG <= 18 ------------(iii)

    (ii) minus (iii),
    (0 -0) <= (DEFG -EFG) <= (28 -18)
    0 <= DE <= 10 ----------------------***

    That means, between D and E, the possible distance is from 0 to 10 km. ---------answer.
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