We study the reach control problem for affine systems on simplices, and the focus is on cases when it is known that the problem is not solvable by continuous state feedback. In previous work we used the reach control indices to construct a (discontinuous) piecewise affine control that solves the problem. Here we investigate the extent to which time-varying feedbacks can be used. A simple time-varying affine feedback is proposed and shown to solve the problem. (c) 2013 Elsevier Ltd. All rights reserved.