GPS systems typically do not factor in posted speed limits when calculating arrival times. Instead, they primarily rely on the current speed of the vehicle, obtained through the GPS receiver's measurements of the vehicle's movement. By tracking the changes in the position of the vehicle over time, the GPS system can estimate the speed at which the vehicle is traveling.
The estimated speed, along with the distance remaining to the destination, is then used to calculate the estimated time of arrival (ETA). This calculation is typically based on the assumption that the vehicle will continue to travel at the current speed until it reaches the destination. It does not take into account any speed limits or traffic conditions along the route.
It's worth noting that some advanced GPS systems may incorporate real-time traffic information to adjust the estimated arrival time based on current traffic conditions. However, even in such cases, the speed limits themselves are not directly factored into the calculation.