Who wins this race?

[md65536]

Suppose two snails are having a race.

They both start out at a speed of 1m per day, but they both will slow down:

After every hour, snail A reduces its speed by half.

After every milliimeter covered, B reduces its speed by half.

 

If the race is 1m long, who would win?

[imatfaal]

Great question - head full of thoughts but not enough maths. Will put down thoughts later.

 

I hope this is close to being correct

 

 

 

the snail that reduces its speed every hour never makes it - as race time approaches infinity he has done 83 1/3 mm

- distance equals the infinite sum of a geometric series with a being 3600 * 1000/(60*60*24) and r being 1/2

 

the snail that reduces its speed every millimetre will take many times the age of the universe but as each millimetre takes a finite time he will eventually make it (10^303 seconds)

- the time being the sum to thousand terms of geometric series with a being (24*60*60)/1000 and r being 2

 

so the snail that reduces every millimetre wins - but the universe is in heat death by then!

 

 

 

 

hope there were no mistakes

[md65536]

Great question - head full of thoughts but not enough maths. Will put down thoughts later.

 

I hope this is close to being correct

That's correct to the best of my knowledge.

 

 

 

Snail A never makes it past twice the distance it travels in the first hour.

 

Snail B can travel arbitrarily far (lightyears, if it could continue for unfathomable lengths of time). After traveling any distance, it will have spent over half its time traveling the last millimeter. Each millimeter doubles the required time.

 

 

 

 

 

 

[Guest lab_supplies]

Great brainteaser. I love problems that have to deal with math.

[Axioms]

In reality. . .

 

 

 

Both snails would not finish. Theoretically the snail that has a decrease in speed per mm would eventually finish.