Vagueness and the Aftermath - A sporadic diary

[tikay]

Tal.

Am I reading this wrong?


e.g., 7.35?

[doubleup]

haven't considered Tal's post

I think that you just need to work out the first point they cross as it will be the same time after that till the next cross etc

So the problem is "when will thing one, moving at 60 times the speed of thing two, and starting 60 units behind thing two, catch thing two.  I think that you can work it out using calculus if you define an equation.  I vaguely remember you get some sort of paradox if you try to calculate it manually in bits. ie thing one never catches thing two because you keep using tinier and tinier distances.

edit

A tortoise and a hare have decided to settle once and for all who is the fastest, so they organise a race to be run over 100 metres. The hare, feeling confident, lets the tortoise have a 50-metre head start. The starting pistol goes off, and they both start racing toward the finish. The hare, travelling at twice the speed of the tortoise, reaches the 50-metre mark where the tortoise started. The tortoise, meanwhile, has travelled only 25 metres, so is at the 75-metre mark. The hare then hops to the 75-metre mark, but the tortoise is still slightly ahead, at the 87.5-metre mark. The rabbit again hops to where the tortoise was, but in that time, the tortoise has moved a little bit further still. And so on. No matter how many times the hare tries to catch up, the tortoise remains slightly ahead. And so, Zeno said, the hare can never overtake the tortoise!


https://blogs.unimelb.edu.au/sciencecommunication/2017/10/22/zenos-paradox-the-puzzle-that-keeps-on-giving/#:~:text=No%20matter%20how%20many%20times,moved%20on%20a%20bit%20further.

[RED-DOG]

I've accidentally invented a maths problem and now it's bugging me because I don't know how to work out the answer.

In 12 hours the minute and hour hands on a clock align perfectly with each other 12 times but what, precisely, are those times?

I know the first, (or last) one is 12:00 if that helps..

They overlap 13 times in 12 hours: once every 65 minutes.

12:00
1:05
2:10
3:15
4:20
5:25
6:30
7:35
8:40
9:45
10:50
11:55
12:00

We're looking for precisely.

At 6:30 the big hand is on the 6 and the little hand is between the 6 and the 7.

it's the same problem to varying degrees for all your answers.

[Doobs]

I've accidentally invented a maths problem and now it's bugging me because I don't know how to work out the answer.

In 12 hours the minute and hour hands on a clock align perfectly with each other 12 times but what, precisely, are those times?

I know the first, (or last) one is 12:00 if that helps..

They overlap 13 times in 12 hours: once every 65 minutes.

12:00
1:05
2:10
3:15
4:20
5:25
6:30
7:35
8:40
9:45
10:50
11:55
12:00

We're looking for precisely.

At 6:30 the big hand is on the 6 and the little hand is between the 6 and the 7.

it's the same problem to varying degrees for all your answers.

I don't think you can count both ends and 11.55 and 12 can't be right.  That one is definitely 12 exact.  I think the gap between must be 12 hours divided by 11, so the first one happens at 1pm + 1/11 of an hour, and the next at 2pm +2/11ths of an hour.  These are exact, putting them into decimals or minutes and seconds makes them less exact. 

[doubleup]

took me ages to do this because of a stupid error

At the simplest it is the intersection of the line on the lol graph below which is the lines y=x and y = 5+5/60x This gives this first point they hit after the hour is on one and the minute on 12.  That is  5.46 minutes So they overlap every 65.46 minutes.

[RED-DOG]

took me ages to do this because of a stupid error

At the simplest it is the intersection of the line on the lol graph below which is the lines y=x and y = 5+5/60x This gives this first point they hit after the hour is on one and the minute on 12.  That is  5.46 minutes So they overlap every 65.46 minutes.

So does that give you actual times?. I want to know what the times are.

[doubleup]

the first time is 5 mins and 27 secs past one. the next is 10 mins and 54 secs past two and so on

It will happen at 10.54 and 33 secs if you can stay awake till then

[RED-DOG]

the first time is 5 mins and 27 secs past one. the next is 10 mins and 54 secs past two and so on

It will happen at 10.54 and 33 secs if you can stay awake till then

If this turns out to be right I'm going to be impressed.

[Doobs]

took me ages to do this because of a stupid error

At the simplest it is the intersection of the line on the lol graph below which is the lines y=x and y = 5+5/60x This gives this first point they hit after the hour is on one and the minute on 12.  That is  5.46 minutes So they overlap every 65.46 minutes.

So does that give you actual times?. I want to know what the times are.

Hark at him, and his demands.  I gave you the exact times, if you want to know the slightly less precise times, doubleup is correct.

[doubleup]

the first time is 5 mins and 27 secs past one. the next is 10 mins and 54 secs past two and so on

It will happen at 10.54 and 33 secs if you can stay awake till then

If this turns out to be right I'm going to be impressed.

I'm all set up for the big reveal

[RED-DOG]

The tension here is palpable.

[RED-DOG]

Boom!

Click to see full-size image.

[doubleup]

I was going to screen grab those clocks but my laptop hasn't got a simple printscreen button, so messed it up.  Anyway its 12 midnight, and then 5 mins 27 secs past one for the next.  I won't stay up for that one, but you're welcome 

[RED-DOG]

I'm truly impressed.   

[tikay]

I'm truly impressed.   

I'd have been much more impressed if you had, well, you know, just looked at your watch in the first place.