In this study, we propose a low-cost power-assisted cart that distributes the torque of a motor using a differential gear and brakes. Carts are designed to help transport heavy payloads and have multiple applications. As the cart size and payload weight increase, cart operation becomes difficult. This led to the development of power-assisted carts, which employ actuators to support the workload. Adding several actuators and high-performance sensors actually increases cart maneuverability; however it increases the cart cost. Commercialization of power-assisted carts warrants that their cost should be decreased without compromising their maneuverability. To this end, we created a power-assisted cart using a motor and a few simple inexpensive sensors. The motor torque is distributed using a differential gear and brakes. However, the characteristics of the differential gear cause an increase in the speed of the cart when turning; hence, we implemented a control algorithm that regulates cart speed during turning. Through experiments, we confirmed that the speed of the cart during turning was kept constant, thereby validating the effectiveness of the developed algorithm.