A transmission and drive system comprises an input end connected to a driving device, an output end connected to a rear wheel, a gear transmission mechanism and a belt driven transmission mechanism. A unidirectional transmission mechanism is connected to the rear wheel with the unidirectional transmission mechanism driving the rear wheel. The transmission provides power output by the driving device, transmits power to the pulley transmission mechanism by the gear transmission mechanism, and the pulley transmission mechanism drives the rear wheel to rotate the unidirectional transmission mechanism, such that the vehicle moves forward. Noise dampening plates are provided to reduce noise emanating from the transmission. In addition, a belt tensioning system is provided to maintain consistent tension on the belt.