Comment by gblargg
6 months ago
The idea that these will keep being improved on in speed reminds me of the math problem about average speed:
> An old car needs to go up and down a hill. In the first mile–the ascent–the car can only average 15 miles per hour (mph). The car then goes 1 mile down the hill. How fast must the car go down the hill in order to average 30 mph for the entire 2 mile trip?
Past improvement is no indicator of future possibility, given that each improvement was not re-application of the same solution as before. These are algorithms, not simple physical processes shrinking.
Is the downhill section a cliff? Google informs me terminal velocity of a car is 200-300mph, so to fall a mile at 300mph, the car will need 12 seconds, so let's round up to 15 seconds to account for the time it's accelerating.
To cover the full 2 miles at an average of 30mph, we need to complete the entire journey in 4 minutes, leaving 225 seconds for the ascent.
We know that the old car was averaging 15 miles per hour, but the speedo on an old car is likely inaccurate, and we only need to assume a 6% margin of error for the car to show 15 miles per hour and cover the mile in 225 seconds. You probably couldn't even tell the difference between 15 and 16 on the speed anyway, but let's say that we also fitted out the car with brand new tyres (so the outer circumference will be more than old worn tyres), and it's entirely possible.
So, let's say 240mph. That's the average speed of our mile freefall in 15 seconds.
41 mph, assuming the person asking the question was just really passionate about rounding numbers and/or had just the bare minimum viable measurement tooling available :)))
I'm afraid your maths doesn't add up, so you've missed their point: it can't be done.
To average 30mph over 2 miles, you need to complete those 2 miles in 4 minutes.
But travelling the first mile at 15mph means that took 4 minutes. So from that point the only way to do a second mile and bring your average to 30mph is to teleport it in 0 seconds.
(Doing the second mile at 41mph would give you an average speed of just under 22mph for the two miles.)
Of course.
My math only "checks out" if you accept and account for the additional assumption I made there: that the datapoints provided in the question have been rounded or were low resolution from the get-go.
The motivation behind this assumption is twofold: the numbers in the question are awfully whole (atypical for any practical problem), and that just the rote derivation of it all doesn't produce very interesting results (gives you the infinite speed answer). :)
Try introducing some error terms and see how the result changes! It's pretty fun, and it's how I was able to eek out that 41 mph result in the end.
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