Motivated by the observation of two distinct superconducting phases in the moireless ABC-stacked rhombohedral trilayer graphene, we investigate the electron-acoustic-phonon coupling as a possible pairing mechanism. We predict the existence of superconductivity with the highest T-c similar to 3 K near the Van Hove singularity. Away from the Van Hove singularity, T-c remains finite in a wide range of doping. In our model, the s-wave spin-singlet and f-wave spin-triplet pairings yield the same T-c, while other pairing states have negligible T-c. Our theory provides a simple explanation for the two distinct superconducting phases in the experiment and suggests that superconductivity and other interaction-driven phases (e.g., ferromagnetism) can have different origins.