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First, this is my first post in math.se, if this question is not adequate to this site, please show me where it would be fit ok ? And sorry in avance.

Yesterday I was seeing a video in YouTube in enhanced speed and tried to calculate how long the rest of the video would take in the speed I was playing. Surprisingly I got that task reaveled harder for me than I thought.

Let's say it's an hour long video and I'm seeing it in a 1.25x speed.

AFAIU the first thing I thought, is that this should be a very basic rule of three: 1 speed - 60 minutes, 1.25 - X. No... this results in 75. Longer than the video.

So I thought in another approach: 60/1,25 = 48. That's better. But 60/1,5 if 40. Shouldn't it be 45 ? because if at 2x 60 minutes should be 30. Then AFAIU 1,5x should be 45 minutes. Isn't that it?

So finally I thought in inverting it: 60/45 = 0,75 (6/8) which should be the correct value for 1,5x. And 60/30 = 0,5 (4/8) so 1,25 should be (7/8) which is 52,5 which in half between 45 and 60 minutes. Seems correct.

So in a table:

1x      1 (8/8)       60
1,25x   0,875 (7/8)   52,5
1,5x    0,75  (6/8)   45
1,75x   0,625 (5/8)   37,5
2x      0,5 (4/8)     30

But this has 2 problems. If I continue the above to slower speeds, this won't work:

0,75x   1,125 (9/8)   67,5
0,5x    1,25 (10/8)   75  <- should be 120

And even if it worked how do I create a formula to relate 1st and 2nd columns so I can calculate the value to any speed.

At this point I was so confused that I had to ask you fine people of math studies.

How do I calculate how much a video will take if I change speed ?

Thanks :)

Nelson Teixeira
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    "But 60/1.5 is 40. Shouldn't it be 45?" Why do you think it should be 45? Because 45 is halfway between 30 and 60? And 1.5 is halfway between 1 and 2? No. This is not linear. You have it correct, it really is 40 and not 45 here. – JMoravitz Sep 28 '22 at 16:54
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    $\text{speed} = \frac{\text{distance}}{\text{time}} \implies \text{time} = \frac{\text{distance}}{\text{speed}}$, here distance is equivalent to the original time left. You were correct the first time. To understand it better, ask yourself should 3x speed give you 20 minutes, or 0 minutes according to your table? – EnEm Sep 28 '22 at 16:56
  • I understand. But then... what's the formula ? time/speed ? just that ? Thinking again 60/1 = 60 OK, 60/1,25 = 48 OK, 60/1.5 = 40 OK, 60/2 = 30, OK and 60/3 = 20, OK. Just that ? – Nelson Teixeira Sep 28 '22 at 17:26
  • Yes... just that. – JMoravitz Sep 28 '22 at 17:55
  • LOL. I as we say around here I was looking for horns in a horse's head. Thanks. :) Don't you want to write an answer so I can accept ? I won't delete the question as I have another one related to this that a little better. Will post later. – Nelson Teixeira Sep 28 '22 at 18:18

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