[tex]u = 1 - \dfrac{3v}{vt-w} [/tex]
[tex]\dfrac{3v}{vt-w} = 1 - u[/tex]
[tex]3v = (1 - u)(vt - w)[/tex]
[tex]3v = vt - w - uvt + wu[/tex]
[tex]vt - uvt = 3v + w - wu[/tex]
[tex]t(v - uv) = 3v + w - wu[/tex]
[tex]t = \dfrac{3v + w - wu}{v - uv} [/tex]
