Real-time time-dependent density functional theory (RT-TDDFT) is a powerful tool for obtaining spectroscopic observables and understanding complex, time-dependent properties. Currently, performing RT-TDDFT calculations on large, fully quantum mechanical systems is not computationally feasible. Previously, polarizable mixed quantum mechanical and molecular mechanical (QM/MMPol) models have been successful in providing accurate, yet efficient, approximations to a fully quantum mechanical system. Here we develop a coupling scheme between induced dipole based QM/MMPol and RT-TDDFT. Our approach is validated by comparing calculated spectra with both real-time and linear-response TDDFT calculations. The model developed within provides an accurate method for performing RT-TDDFT calculations on extended systems while accounting for mutual polarization between the quantum mechanical and molecular mechanical regions.