md65536 Posted October 20, 2011 Share Posted October 20, 2011 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? 1 Link to comment Share on other sites More sharing options...
imatfaal Posted October 20, 2011 Share Posted October 20, 2011 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 Link to comment Share on other sites More sharing options...
md65536 Posted October 20, 2011 Author Share Posted October 20, 2011 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. Link to comment Share on other sites More sharing options...
Guest lab_supplies Posted October 24, 2011 Share Posted October 24, 2011 Great brainteaser. I love problems that have to deal with math. Link to comment Share on other sites More sharing options...
Axioms Posted October 28, 2011 Share Posted October 28, 2011 In reality. . . Both snails would not finish. Theoretically the snail that has a decrease in speed per mm would eventually finish. Link to comment Share on other sites More sharing options...
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