Poetry with Numbers -- from Lewis Carroll

     One of the timeless treasures on my bookshelves is a complete collection of work by Lewis Carroll (pen name for Charles Lutwidge Dodgson, 1832-1898) -- writer, puzzler, math guy . . . Here's a poem I found in "Answers to Knot 1" in A Tangled Tale.  (The problem, Knot 1, is stated below the poem.)

from   A Tangled Tale     a response (by authors named below) to a puzzle posed by Lewis Carroll

        The elder and the younger knight
           They sallied forth at three;
        How far they went on level ground
           It matters not to me;
        What time they reached the foot of hill,
           When they began to mount,
        Are problems which I hold to be
           Of very small account.

       The moment that each waved his hat
           Upon the topmost peak --
        To trivial query such as this
           No answer will I seek.
        Yet can I tell the distance well
           They must have travelled o'er:
        On hill and plain, 'twixt three and nine,
           The miles were twenty-four.

       Four miles an hour their steady pace
           Along the level track,
       Three when they climbed -- but six when they
           Came swiftly striding back
        Down the hill; and little skill
           It needs, methinks, to show,
        Up hill and down together told,
           Four miles an hour they go.

       For whether long or short the time
           Upon the hill they spent,
       Two thirds were passed in going up,
           One third in the descent.
       Two thirds at three, one third at six,
          If rightly reckoned o'er,
       Will make one whole at four -- the tale
          Is tangled no more.                          SIMPLE SUSAN, MONEY SPINNER

Here's a statement of the problem, Knot 1, for which the lines above by SIMPLE SUSAN and MONEY SPINNER offer a solution; two travelers spent from 3 o'clock till 9 walking along a level road, up a hill, and home again; their pace on the level was 4 miles an hour, up hill 3, and down hill 6.  Find the distance walked; also (within half an hour) the time of reaching top of hill.