By definition of average velocity,
[tex]v_{\rm ave} = \dfrac{\Delta x}{\Delta t} = \dfrac{115\,\mathrm m}{\Delta t}[/tex]
If this object is under constant acceleration, then average velocity is also equal to the average of the initial and final velocities:
[tex]v_{\rm ave} = \dfrac{v_f+v_i}2 = \dfrac{5.00\frac{\rm m}{\rm s}+4.20\frac{\rm m}{\rm s}}2 = 4.60\dfrac{\rm m}{\rm s}[/tex]
Then the time it takes for the object to travel 115 m with this average velocity is
[tex]4.60\dfrac{\rm m}{\rm s} = \dfrac{115\,\mathrm m}{\Delta t} \implies \Delta t = \boxed{25\,\mathrm s}[/tex]
