We aim to evaluate analytically the age of the surface water (i.e., the time elapsed since last touching the water-air interface) in a steady-state, water column model with constant (vertical) diffusivity. We calculate CART's passive tracer or surface water age and a radio-age, which is obtained from the concentration of a passive tracer and a decaying one (first order decay). The previous age is greater than the latter, except at the sea surface, where all ages are prescribed to be zero. The difference between these ages increases as the rate of decay increases. The radio-age is asymptotic to CART's age for small values of the Damköhler number, which is the ratio of the diffusion timescale to the decay timescale.