ABSTRACTThe ‘spectral age problem’ is our systematic inability to reconcile the maximum cooling time of radiating electrons in the lobes of a radio galaxy with its age as modelled by the dynamical evolution of the lobes. While there are known uncertainties in the models that produce both age estimates, ‘spectral’ ages are commonly underestimated relative to dynamical ages, consequently leading to unreliable estimates of the time-averaged kinetic feedback of a powerful radio galaxy. In this work, we attempt to solve the spectral age problem by observing two cluster-centre powerful radio galaxies; 3C 320 and 3C 444. With high-resolution broad-band Karl G. Jansky Very Large Array observations of the radio sources and deep XMM–Newton and Chandra observations of their hot intracluster media, coupled with the use of an analytic model, we robustly determine their spectral and dynamical ages. After finding self-consistent dynamical models that agree with our observational constraints, and accounting for sub-equipartition magnetic fields, we find that our spectral ages are still underestimated by a factor of two at least. Equipartition magnetic fields will underestimate the spectral age by factors of up to ∼20. The turbulent mixing of electron populations in the radio lobes is likely to be the main remaining factor in the spectral age/dynamical age discrepancy, and must be accounted for in the study of large samples of powerful radio galaxies.