- 07 Jun '05 19:05OK, here's a relatively simple puzzle. Say there's an ant trying to burrow through a slab of dirt 1 metre thick. The ant crawls at 0.2 metres per second, and digs at a rate of (1/60) m/s. The ant must also carry all the dirt it removes out to the entrance to make room for more tunneling. How fast can it dig through the slab?
- 07 Jun '05 21:20

Hmm. Actually, this is a stupid puzzle. There's no defined answer. Consider this one instead: the ant digs up chunks 0.01 metres deep. Now how long does it take to burrow through?*Originally posted by PBE6***OK, here's a relatively simple puzzle. Say there's an ant trying to burrow through a slab of dirt 1 metre thick. The ant crawls at 0.2 metres per second, and digs at a rate of (1/60) m/s. The ant must also carry all the dirt it removes out to the entrance to make room for more tunneling. How fast can it dig through the slab?** - 07 Jun '05 22:44

The quickest way is for it to burrow all the way through and then carry all the dirt out.*Originally posted by PBE6***OK, here's a relatively simple puzzle. Say there's an ant trying to burrow through a slab of dirt 1 metre thick. The ant crawls at 0.2 metres per second, and digs at a rate of (1/60) m/s. The ant must also carry all the dirt it removes out to the entrance to make room for more tunneling. How fast can it dig through the slab?**

This would take 60 secs + 5 secs = 65 secs - 07 Jun '05 22:51

It has to dig up one metre, that takes 60s*Originally posted by PBE6***Hmm. Actually, this is a stupid puzzle. There's no defined answer. Consider this one instead: the ant digs up chunks 0.01 metres deep. Now how long does it take to burrow through?**

the time it has to spend walking is the sum from n=1..100 of n/10 which is 50.5*100/10, i.e 505s

so I make it that the ant takes a total of 565s - 07 Jun '05 23:13 / 1 edit

Walking time = 50.5m * 5s/m = 252.5s*Originally posted by iamatiger***It has to dig up one metre, that takes 60s**

the time it has to spend walking is the sum from n=1..100 of n/10 which is 50.5*100/10, i.e 505s

so I make it that the ant takes a total of 565s

edit:

oops - I forgot that the ant has to walk back down after removing the dirt, making it 101m of total walking distance, and 565s total time, as you already stated.