Loading a video on the internet

[guss]

This isn't a homework problem, but I'm going to make it sound like one because I think that's the best way to explain it.

An hour-long video on the computer loads 1/3rd of a second of footage every second. The video can be played while it is loading.

a)What is the minimum amount you have to wait, if the video has just begun loading, before you can play the whole video uninterrupted (as in, without having to wait for it to load)?

b)If you wait 4 minutes, then play the video, how long until the video gets interrupted and requires more footage to be loaded?

They are supposed to be tricky because (for example in b) while you are playing the first 4 minutes of footage, more footage will continue to load. And while you are playing that footage, even more footage will load. And so on.

I think the solution to this problem is probably simple, I'm just curious on how to do it.

 

[Mentallic]

You can convert these kinds of problems into algebraic expressions. For example, let's define x to be minutes passed and y to be the length of footage.

For the video loading, it would be described by $y=x/3$ because as every minute passed, 1/3 of the footage has been loaded. At y=60 (60 minutes of footage) x=180 (minutes taken to load the video).

For watching the video, we can describe it by $y=x-c$ (c is some constant that represents the time at which we start watching) because for every minute watched, a minute of footage passes.

Now we find the intersection of these lines and substitute in a value of x or y that we know, but an easier way is just to take the second equation and let y=60, x=180 then 60=180-c, thus c=120. So to watch the video without waiting for it to load we need to start watching at least 2 hours into the loading.

Can you try the second question?

 

[gsal]

Yeah, this is pretty simple...

In particular, part 'a' can be solved by simple reasoning...basically, it takes 3 times as long to download than to watch, so, a 1-hour long video is going to take 3 hours to download; if you want to watch it uninterrupted, you need to start 1 hour before it finishes downloading...that is, you need to start watching 2 hours into the download.

Part 'b' is best solved by drawing two lines and finding the intersection...the first (downloading) line starts at the origin with a slope of 1/3...the watching line starts at the 4 minute mark with a slope of 1 ...find the intersection and that's when you need to wait for more download.

 

[guss]

Thanks guys! Makes a lot of sense now. I was wayyy over thinking this problem. A way I thought of to solve b soon after I made this post was to do this infinite sum:

$\sum\limits_{i=0}^\infty 4(\frac{1}{3})^i$

Which would give 6 minutes. But now I see it's more simple than that.

 

[Mentallic]

Thanks guys! Makes a lot of sense now. I was wayyy over thinking this problem. A way I thought of to solve b soon after I made this post was to do this infinite sum:

$\sum\limits_{i=0}^\infty 4(\frac{1}{3})^i$

Which would give 6 minutes. But now I see it's more simple than that.

Ahh I'm not surprised you had this approach infused in your head. Since the start you were worried about the continuous loading as you watched:

while you are playing the first 4 minutes of footage, more footage will continue to load. And while you are playing that footage, even more footage will load. And so on.