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A video with $30$ minutes length, played at $33.33\%$ faster speed that equates to $22.5$ minutes. Where are the extra $2.508$ minutes?

Yes the math is $$\frac{30}{1.3333} = 22.50,$$ but my intuition is that the result should be $20$ minutes. How do we reconcile that "$2.5$" minutes extra?

Xander Henderson
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Andy
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    Why "intuitively" should the answer be $20$ minutes? – David G. Stork Jul 14 '20 at 21:14
  • Let's go through a simpler example. Let's say that the video is played at $100%$ faster speed, i.e. $2 \times$ speed. Then I think there's no intuitive issue concluding the video is

    $$\frac{30 \text{ min.}}{2} = 15 \text{ min.}$$

    long. So what if the video is $30%$ faster, i.e. $1.3 \times$ speed? The same sort of calculation gives its length as

    $$\frac{30 \text{ min.}}{1.3} \approx 23.077 \text{ min.}$$

     – PrincessEev Jul 14 '20 at 21:19
  • On the other hand, this begs a question: at what speed we will play the video at to get $20$ minutes? If we set up the proportion, we see

    $$\frac{30 \text{ min.}}{x} = 20 \text{ min.} \implies x = \frac{30 \text{ min.}}{20 \text{ min.}} = 1.5$$

    i.e. the video would have to be played $50%$ faster. I don't really see how this is unintuitive.

     – PrincessEev Jul 14 '20 at 21:20
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    Why the downvotes? OP shared reasoning and steps taken, even if flawed. Isn't that the point of asking? – DreiCleaner Jul 14 '20 at 21:34
  • @ David G. Stork, "intuitively" because if the video is 30 mins long and it played a third faster. Therefore the last third of video would have been negate due to faster speed. So only 20 mins would have get accounted. – Andy Jul 14 '20 at 22:51
  • @DreiCleaner: Look at the revision history. Don't assume that downvoters have no good reason. (By the way I wasn't even one of them.) – user21820 Jul 18 '20 at 17:38

1 Answers1

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You have two problems. I think you are trying to say that if it is played $\frac 13$ faster you expect it to be done in $20$ minutes. First, $\frac 13$ faster is $33.3\overline 3\%$ faster, not $30\%$ faster. That would make the running time $\dfrac {30}{\frac43}=22.5$ minutes. The second is that if you want to reduce the running time from $30$ to $20$ minutes, you need to go $50\%$ faster. As you are reducing the time by a factor $\frac 23$ you need to increase the speed by a factor $\frac 32$

Ross Millikan
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