We propose a novel, economical multi-rate all-optical packet clock extraction scheme of return-to-zero code, which comprises a Fabry-Pérot (F-P) filter, a semiconductor optical amplifier (SOA) and polarization dependent delay interferometers (PDIs). Fabry-Pérot (F-P) filter with low finesse and low free spectral range was used to directly extract the multi-rate packet clock from the packet data stream, which ensures that the clock establishes and vanishes quickly. Different PDIs, combined with F-P filter was used to form comb filters with different FSRs to extract mult-rate packet clock. The packet clock then goes into SOA to reduce the low-frequency amplitude noise and temporal fluctuation with the self-gain modulation effect of SOA. We demonstrate instantaneous 10 GHz, 20 GHz and 40 GHz packet clock extraction experimentally by switching different PDI and forming filters with different FSR. Multi-rate packet clock signals with high quality and low temporal fluctuation are obtained.