Cell-free massive multiple-input multiple-output (MIMO) is a potential key technology for fifth generation wireless communication networks. A mixed quality-of-service (QoS) problem is investigated in the uplink of a cell-free massive MIMO system where the minimum rate of non-real time users is maximized with per user power constraints whilst the rate of the real-time users (RTUs) meet their target rates. First an approximated uplink user rate is derived based on available channel statistics. Next, the original mixed QoS problem is formulated in terms of receiver filter coefficients and user power allocations which can iteratively be solved through two subproblems, namely, receiver filter coefficient design and power allocation, which are dealt with using a generalized eigenvalue problem and geometric programming, respectively. Numerical results show that with the proposed scheme, while the rates of RTUs meet the QoS constraints, the 90%-likely throughput improves significantly, compared to a simple benchmark scheme.