This paper reports the development of a method to control the flow rate of fluids within paper-based microfluidic analytical devices. We demonstrate that by simply sandwiching paper channels between two flexible films, it is possible to accelerate the flow of water through paper by over 10-fold. The dynamics of this process are such that the height of the liquid is dependent on time to the power of 1/3. This dependence was validated using three different flexible films (with markedly different contact angles) and three different fluids (water and two silicon oils with different viscosities). These covered channels provide a low-cost method for controlling the flow rate of fluid in paper channels, and can be added following printing of reagents to control fluid flow in selected fluidic channels. Using this method, we redesigned a previously published bidirectional lateral flow pesticide sensor to allow more rapid detection of pesticides while eliminating the need to run the assay in two stages. The sensor is fabricated with sol-gel entrapped reagents (indoxyl acetate in a substrate zone and acetylcholinesterase, AChE, in a sensing zone) present in an uncovered "slow" flow channel, with a second, covered "fast" channel used to transport pesticide samples to the sensing region through a simple paper-flap valve. In this manner, pesticides reach the sensing region first to allow preincubation, followed by delivery of the substrate to generate a colorimetric signal. This format results in a uni-directional device that detects the presence of pesticides two times faster than the original bidirectional sensors.