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 Waiting, waiting... (Posted on 2004-08-07)
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!

 See The Solution Submitted by Federico Kereki Rating: 3.2857 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Slightly different solution | Comment 2 of 19 |

I agree with Juggler that for the first table, they will have to wait 1.5 minutes (60 minutes/40 tables).  After the first couple is seated though, we should only consider 39 tables, because the 40th table has just been seated and is not about to finish.  So we should add 60/39 minutes for the next couple and 60/38 for the next and so on until we add 60/22.

Calculating that on a calculator, I get 37.99106005 minutes.  I'll just round that off to 38 minutes.

Actually, rethinking this, something doesn't seem quite right.  Anyone care to show this wrong?

Edited on August 7, 2004, 12:20 pm
 Posted by Tristan on 2004-08-07 12:18:59

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