The optical transmission characteristics in a ring cavity optomechanical system with two special paths are investigated. The structures of the two paths are independent of each other, but there are phonon and photon couplings between them. By adjusting the coupling intensity and the effective optomechanical coupling rate of the two independent coupling paths, the system shows the tunability of induced transparency. When the coupling intensity is large, the transparent peak of symmetric detuning point will be produced. And the distance and intensity of the transparent peak can be regulated by coupling intensity of the two paths, which makes the all-optical switching based on the system feasible in theory. In addition, the group delay of transmitted light can be easily changed by adjusting the relevant parameters, and the tunability of fast and slow light can be realized by many ways. Under some conditions, the system shows the excellent characteristics of fast and slow light modulation, which will provide a good platform for the fabrication of related photonic devices and the research of quantum phenomena.