Using the entire OPAL LEP1 on-peak Z hadronic decay sample, Z --> qqbar gamma decays were selected by tagging hadronic final states with isolated photon candidates in the electromagnetic calorimeter. Combining the measured rates of Z --> qqbar gamma decays with the total rate of hadronic Z decays permits the simultaneous determination of the widths of the Z into up- and down-type quarks. The values obtained, with total errors, were Gamma_u = 300 ^+19_-18 MeV and Gamma_d = 381 +- 12 MeV. The results are in good agreement with the Standard Model expectation.