It is a snowy day at Logan airport. After leaving the gate, all planes must go t

Question

It is a snowy day at Logan airport. After leaving the gate, all planes must go through a de-icing process before going to the runway to take off. After waiting in line, it takes approximately 10 minutes to actively de-ice each plane. After being de-iced, planes proceed to an area where they wait in line to take off an average of 15 minutes. Planes then take 60 seconds to take off. On average 14 planes are waiting to be deiced and 9 planes are waiting to take off. 36 planes leave the gate every hour (on average). What is the total time a plane spends in this process (until it is in the air)? How many planes are in the deicing portion of this process (wait and process time)?

Explanation / Answer

1. The total time a plane spends until it is in the air = De-icing time + Waiting in line time + take off time

= 10 mins + 15 mins + 60 secs (1 min)

= 26 mins

2. Total number of planes that are in the de-icing portion of this process are calculated as follows:

Number of planes leaving the gate every hour = 36

Average number of planes waiting to be de-iced = 14

Average number of planed waiting to take off = 9

Hence total planes waiting for deicing portion of this process = (25/23)*36 = 39.13

= 39.13/23 = 1.7

Therefore 1.7 planes are in the de-ice process

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