Turtle vs The Speedster

Let our minimum waiting time be $x$ minutes, in which when we return $\frac{x}{5}$ minutes of video will be loaded. After playing these $\frac{x}{5}$ minutes, we will have another $\frac{x}{25}$ minutes loaded. We notice a geometric progression in the minutes loaded in the intervals we have watched, thus showing the total time that we can watch without pausing to be:

$\frac{x}{5}+\frac{x}{25}+\dots=x\cdot(\frac{1}{5}+\frac{1}{25}+\dots)=\frac{x}{4}=100$

$\Rightarrow x = 4\cdot 100=\boxed{400}$

The Time you needed to fully load the video is 500 Minutes , but however we want to start playing anyways but in the same time make sure that if the browsing turtle speed was at 70% or 80% or what so ever from the video time until the speedster who is yourself reaches there , the turtle should reach the end of the video ... so that being said , by waiting 400 minutes the turtle currently at 80 minutes so it needs another 20 minutes to fully load the video which is exactly the time that will be used next , you will play the video after waiting 400 minutes , so that you made sure that there will be no pauses