\documentclass{article}

\usepackage{ltablex}

\textheight=4in

\begin{document}

% we want a table that is \textwidth long, has 4 columns, columns 1
% and 3 are auto sized with the 3rd columns being 3 times wider than
% the first column.
%

\begin{tabularx}{\linewidth}%
 {|>{\setlength{\hsize}{.5\hsize}\raggedright\arraybackslash}X| % col 1; auto-sized ragged right
    c|                                                        % col 2; default    centered
    >{\setlength{\hsize}{1.5\hsize}\raggedleft\arraybackslash}X|% col 3; auto-sized ragged left
    l|}                                                       % col 4; default    left-justified

\caption*{The Table Caption}\\
\hline
F-Head1 & F-Head2 & F-Head3 & F-Head4\\
\hline
\hline
\endfirsthead
\hline
Head1 & Head2 & Head3 & Head4\\
\hline
\hline
\endhead

\hline
\hline
Foot1 & Foot2 & Foot3 & Foot4\\
\hline
\endfoot

\hline
\hline
L-Foot1 & L-Foot2 & L-Foot3 & L-Foot4\\
\hline
\endlastfoot

This is a very long sentence not likely to fit&
not too long&
This is another  very long sentence not likely to fit&
not long\\

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