how fast are radio waves?

i know that they are suppose to go as fast as light, but.....
then i though, if it's really that fast, then how do the GPS works?
cuz GPS works by 3 satellites pinging at the same time with their location with it, therefore, with the calculation of the difference in time reviving the pings, it can work out accurately where is the device in terms of the 3 satellites.
now here comes the question,
there is nothing faster than light, then how can the machine tell the difference in the time that it receive the pings?
what i want to know is that, if i use a radio wave sender, and have a sending and a reviving at both ends; both of which are an arms' length apart (1.3m apart)
can it calculate the distance in between? and what i they were even closer?