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?

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?

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?

The quickest way is for it to burrow all the way through and then carry all the dirt out.

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?

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

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

Walking time = 50.5m * 5s/m = 252.5s

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.