maximum speed of cheetah is
[tex]v_1 = v_{max}[/tex]
speed of gazelle is given as
[tex]v_2 = v_{g}[/tex]
Now the relative speed of Cheetah with respect to Gazelle
[tex]v_{12} = v_1 - v_2[/tex]
[tex]v_{12} = v_{max} - v_g[/tex]
now the relative distance between Cheetah and Gazelle is given initially as "d"
now the time taken by Cheetah to catch the Gazelle is given as
[tex]d = v_{12}* t[/tex]
so by rearranging the terms we can say
[tex]t = \frac{d}{v_{12}}[/tex]
[tex]t = \frac{d}{v_{max} - v_g}[/tex]
so above is the relation between all given variable