You are outside a well known restaurant, waiting in queue, with 18 couples in front of you. You know there are forty tables inside, and you think an average meal will take one hour.

How long will you have to wait, on average?

PS. This problem comes from queueing theory, but you don't have to know anything about it to find the answer!

(In reply to Slightly different solution by Tristan)

I see what I did wrong.  I am correct in decreasing the table number for every couple seated, but I am also supposed to decrease the waiting time per table.  Considering only the people seated before I got in line, if everyone is average, no one will eat for more than 60 more minutes.  After the first couple in line is seated, 1.5 minutes have passed, and all the people eating won't be eating for more than 58.5 minutes.  So the correct number of minutes for the next couple to wait is actually 58.5/39 minutes.  This is equal to 1.5 minutes!

If you calculate the rest of the couples, you'll see that each will wait 1.5 minutes.  So I now agree with Juggler's answer of 28.5 minutes.

Posted by Tristan on 2004-08-07 12:35:59