By definition of average acceleration,
[tex]\bar a=\dfrac{\Delta v}{\Delta t}[/tex]
[tex]\implies15.0\,\dfrac{\mathrm m}{\mathrm s^2}=\dfrac{160.0\,\frac{\mathrm m}{\mathrm s}-100.0\,\frac{\mathrm m}{\mathrm s}}{\Delta t}[/tex]
[tex]\implies\Delta t=4.00\,\mathrm s[/tex]
