Job interview question and answer: How many people are there flying in airplanes over the US right now?

Posted October 13, 2011, by Josie Chun

This is an example of a case interview question – the type used by management consultancies and sometimes investment banks when recruiting. The purpose of such questions is to see your logic and ability to identify crucial issues when tackling a complex problem.

Ex-management consultant and now Director of Strategy and Innovation for Inchcape Australia, Stephen Scheeler, takes us through his step-by-step approach in answering this question. Remember, there is no ‘correct’ answer or one way of answering, and the number you come up with is not as important as how you go about finding it. Following Scheeler’s thought processes will help you to see how this sort of question can be broken down into key variables and assumptions, as well as how to go about articulating your logic.

‘The key here is to think about what information you have (or can estimate) which can help you get to the answer. You need to be clear about your logic and assumptions, and be clear-minded enough to be able to sense-check the ultimate answer you arrive at.

First, I clarify the question – what is meant by “airplanes”? All planes, private jets, commercial flights only, military, fly-overs? And what is meant by “right now” – literally right this second? What is meant by “over the US”? Landmass only? Does this include ocean territory? What about Alaska and Hawaii?
I will assume that “airplanes” can be divided into four categories: commercial passenger, freight, small private and military. There will be other types (like charters and crop-dusters) but to simplify things I will leave them aside.
I assume that these flights are only those flying domestically or to an international destination (but still over the US). I will exclude planes flying over the US from one country to another.
I assume that “right this second” means 6.45pm.
I assume that “over the US” means over the landmass of the contiguous 48 states.
Then I look at each type of plane to look for drivers of the ultimate number.
For commercial passenger planes, I assume a good driver would be the number of airports in the USA. I assume there are:
10 giant airports
20 major airports
50 medium airports
100 small airports
Giant airports would have about 20 flights per hour taking off, 18 hours per day. So, about 360 flights per day. At any one time, perhaps 15 per cent of these flights would be in the air. I would assume that the average plane would contain 250 people. So, that's 360 x 15% x 250 x 10 airports = 135 000 people.
Major airports would have about 10 flights per hour, 18 hours per day. Fifteen per cent would be in the air at any one time, with an average of 200 people on board. That's 108 000 people.
Medium-sized airports would have about 10 flights per hour, 15 hours per day. Fifteen per cent would be in the air at any one time, with an average of 100 people on board. That's 112 500 people.
Small airports would have about five flights per hour, 12 hours per day. Fifteen per cent would be in the air, with an average of 50 people on board. That's 45 000 people.
Freight is trickier to estimate. I would estimate that there are an average of 100 cargo flights per major city in the US per day, and I'd estimate there are 200 major cities. Fifteen per cent of these flights would be in the air at any one time. They would have an average crew of five. That's 15 000 people.
For small private planes, I'd say there is one private plane for every 500 head of population (300 million people), and that one per cent of these planes might be in the air at any one time, with an average of four people on board. That's 600 000 x 1% x 4 = 24 000 people.
For military I am less sure. Let's assume there are 10 000 military planes in the US (big and small). Let's say five per cent are airborne at any one time with an average of 10 people aboard. That's 5000 people.
Now I can add up all the people. The total equals 444 500 people in the air right now over the US.
To sense-check this, let me just divide by 200 (the average number on board a commercial airliner). That's 2222 planes in the air, or 46 over each of the 48 states.
Hmm, this seems a bit on the high side, so I may have over-estimated somewhere. I can go back through my assumptions and calculations to see if I can trim the number a bit. However, I don't think I'm far off.’

Josie Chun

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