Was told to expect a question like this in an upcoming interview. I've seen market making questions before but not involving measuring distance (usually see ones that involve something more easily guesstimated like population). Can anyone help me come up with a reasonable way to attack this question: How far is it from Chicago to Rome?

As with all these interviews, change it into a math question. Actual accuracy is not important. ie I flew to Spain in college. It was a 7 hour flight. I saw connecting flights to rome that had flight times of 1.5 hours. Assuming 30 minutes is lost on take off and landing, It would be about 7.5 hours to Rome. Planes fly an average speed of 600 mph. 4500 miles between chicago and rome. Always default to realistic assumptions that you can provide a base for with some degree of mathematical computation in your head.

Idea is to show thinking. I've had interviews where I got the problems wrong or couldn't figure it out but still got the offer because when they told me the answer I immediately got it.

I would suggest that the best answer isn't a straight line but the circular path. A line that goes up through canada and down through iceland (like the planes fly). The shortest path on a globe. Unlike a line that goes through Washington DC (like you would on a map).

I'm guessing the posters before me all cheated in one way or another - they got the answer then tried to reverse engineer it: The above approximation would give 6.5 hours => 3,900 miles to Rome, since the take-off and landing has to be applied to the connecting flight as well. It's unusual for outbound flight times to show on monitors. But minmike makes the important point - use assumptions based on whatever you know already. Determine how many significant figures you want for your precision, and always round to the level of at least the same or 1 more sig fig. We round to 2 sig figs: Earth's circumference is about 25,000 miles, so the radius r should be about 4,000 miles. Assume some kind of curvature. A semicircle is the easiest approximation although it's not difficult to do an ellipse if you have a better idea of the Earth's shape. Take the upper quadrants, r' = +sqrt(r^2-x^2). Assume Rome is somewhere along 45 degrees (mainly for ease of computation, since 45/90*2000 = 4e6, but also because Rome is very slightly below New York ~40N but significantly above the equator ~90N). r' = sqrt(16e6 - 4e6) = sqrt(12e6) = 2e3 * sqrt(3). Approximate the circumference around 45N: 2*pi*r' = 4*pi*10^3*sqrt(3). 21e3 miles separate 360 degrees. The error propagation for the remaining part is huge, so this is where you adopt more accuracy with your computation if necessary. There are 24 time zones. 360/24=15 degrees separate each longitude. Standard Eastern time and central European time are separated by 7 hours. If you don't know how close either city is to the edges of the time zone, just give the entire interval. Besides, time zones are not carved accurately according to geographic longitudes. Lower bound sector length: 6*15/360 * 21e3 = 1/4*21e3 = 4,800 miles. Upper bound sector length: 8*15/360 * 21e3 = 1/3*21e3 = 7,000 miles. Rome is between 4,800 to 7,000 miles away from Chicago. I know Chicago is at the edge of the time zone while Rome is around the center, so I'll take a weighted average to arrive at 5,300 miles. The last part is to take a guess at a correction factor: did we over- or under-estimate? Chances are that we probably overestimated because the circumference of Earth that we took is probably at some atmospheric boundary, and the actual ground/flight distance is smaller. Now, question remains whether they want the ground distance or the spatial distance. Ask your interviewer. You can get the latter easily from the former, since by assumption, you have the sector arc length - reverse engineer the angle, and get the base length of the isosceles triangle with that angle and other 2 lengths = radius of Earth.