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## Queuing to C Rioli

A cache by GJMMelb Message this owner
Hidden : 6/25/2017
Difficulty:
Terrain:

Size:  (micro)

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### Geocache Description:

Glenferrie oval is the former home of the Hawthorn Football Club. These days you won't often find Cyril (or any other Hawthorn players) here.  In order to see Hawthorn play you need to join the queue down the road at the MCG.  You can however find a cache nearby by solving the puzzle below.

This scenario is based on a true incident where we missed out on a carpark at the MCG and therefore missed the match!!!

GJMMelb are going to the football at the MCG. They pick up Lochb and Quiet1_au on the way and enter the queue of cars in Hoddle Street 20 minutes before the game.

Assume that cars start arriving at the MCG 2 hours before the game and arrive at a rate which is exponentially increasing up to the start of the game, according to the formulae   λ (arrival rate) = 4(et/60-1) cars per minute, where t =time. Assume that no cars arrive (ie join the queue) after the game starts.

The car park attendants start to serve the cars (ie sell car park tickets) 2 hours before the game and continue until the end of the first quarter, which includes 10 minutes of time-on. At the end of the first quarter the car park is deemed “full” and the gates closed.

Assume the car park attendants consistently take 10 seconds to sell a car park ticket and wave the cars on. Also assume that the 10 seconds includes time for the cars to move up to the car park attendant.

1.How long before the start of the game would GJMMelb, lochb and Quiet1_au need to arrive to avoid a queue of cars? AB

2.How many cars are in the queue ahead of GJMMelb, lochb and Quiet1_au? CDE

3.How long will GJMMelb, lochb and Quiet_au have to wait in the queue of cars? FG.5

4.How much of the first quarter will they miss if it takes 10mins from the time they get a car park ticket until they get to their seats? HI.5

5.How many cars will be turned away from the MCG from this single queue on this gate, when the gate is closed at the end of the first quarter? JKL

6.What is the Utilisation of the parking ‘system’ in Erlangs over the 150 minutes the gate is open? 0. MN

7.How many goals will Cyril Rioli kick in the time GJMMelb, lochb and Quiet1_au are waiting in the queue (creative answers encouraged)?

Answer to one decimal place only (except question 6) and remember there can never be a negative number of cars in the queue.

Using the information above: O=N-I+1 P=M+H Q=C R=F S=B T=A-J-L U=K-J V=E-1 W=G X=D The cache can be found at:

South 37 OP.QRS East 145 TU.VWX

Pnpur vf zvpeb ohg pnzb vf erthyne

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)

Find...

### 8 Logged Visits

4      2      1      1

**Warning! Spoilers may be included in the descriptions or links.