This paper presents a simple synchronous distributed power allocation algorithm that maximizes the total transmission rate of a number of radios operating in an unlicensed band, with either a total power constraint or individual power constraints. The redistribution of power by the algorithm also results in a fairer rate distribution. The algorithm is not based on Game theory or Lagrangian dual. Rather it uses the sensitivity of each user's rate to changes in the power levels of all users in the system, to steer the power distribution towards the global maximum sum rate. The algorithm's complexity scales with the number of users in the system. Simulation results demonstrate that the algorithm does converge to the global maximum sum rate and, at the same time, redistributes the power among the users to achieve a more equitable rate distribution. Results of the algorithm are also compared with solutions based on Game theory.