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We obtain a scaling relation for spherically symmetric k-essence scalarfields $\phi(r,t)$ for an inhomogeneous cosmology with the Lemaitre-Tolman-Bondi (LTB) metric. We show that this scaling relation reduces to the knownrelation for a homogeneous cosmology when the LTB metric reduces to theFriedmann-Lemaitre-Robertson-Walker (FLRW) metric under certain identificationsof the metric functions. A k-essence lagrangian is set up and theEuler-Lagrangian equations solved assuming $\phi(r,t)=\phi_{1}(r) +\phi_{2}(t)$. The solutions enable the LBT metric functions to be related tothe fields. The LTB inhomogeneous universe exhibits accelerated expansioni.e.cosmic acceleration driven by negative pressure.

An accelerated universe with negative equation of state parameter in Inhomogeneous Cosmology with $k$-essence scalar field