We study transmission delay minimization of a wireless powered communication (WPC) system in a point-to-point scenario with one hybrid access point (HAP) and one WPC node. In this type of communications, the HAP sends energy to the node at the downlink (DL) for a given time duration and the WPC node harvests enough radio frequency (RF) power. Then, at the uplink (UL) channel, the WPC node transmits its collected data in a given time duration to the HAP. Minimizing such round trip delay is our concern here. So, we have defined four optimization problems to minimize this delay by applying the optimal DL and UL time durations and also the optimal power at the HAP. These optimization problems are investigated here with thorough comparison of the obtained results. After that, we extend our study to the multiuser case with one HAP and $K$ nodes and two different optimization problems are studied again in these cases.