In this paper, we study the finite-time stability and applications of positive switched linear delayed systems under synchronous impulse control, which includes two types of random switching and average dwell time switching. By constructing a type of linear time-varying co-positive Lyapunov functional, we first propose several new finite-time stability criteria. It should be emphasized that the linear term coefficient of the linear vector of the Lyapunov functional is adjusted to the difference between the weighting vector and the given vector. Then, we apply the obtained stability criteria to the linear time-varying delayed systems with impulsive effects. At last, three examples are given to demonstrate the validity of the obtained results, which includes the specific linear programming algorithm process.