Question

At Chicago O’Hare International Airport, there are an average of 1,042 flights per day. Provethat at least two of these flights must take off within 90 seconds of each other.
(Explain your solution in words as if you were talking to your non-mathematically )

Answer 1

Answer:

Using only the given information, the premise cannot be proven.

Step-by-step explanation:

There are 86400 seconds in a day, so the average length of time between flights is 86400/1042 seconds, about 82.917 seconds. The number of "flights per day" is non-specific as to take-offs and landings. The question specifically asks for a proof related to take-offs.

If one flight takes off and 82.9 seconds later another flight lands and 82.9 seconds later another flight takes off, and so on, the flight schedule can be maintained and take-offs are separated by 165 seconds.

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One can safely assume that O'Hare is neither a source of airplanes, nor their final resting place. Hence the number of take-offs must match the number of landings. For any given airplane at any given airport, the incoming flight number is generally different than the outgoing flight number, so counting flights counts a landing and a take-off as two separate flights.