Estimating the radius of the Earth from a plane trip My friend had an interview at Cambridge. He was asked the following question, and was stumped:

I fly to Chicago. The plane trip is $8$ hours. I look at the time and then set my watch back $6$ hours. Knowing that the Earth rotates $360^\circ$ in $24$ hours, what is the radius of the Earth?

 A: There is not enough information in the question to get anywhere near an estimate of the earth's radius.
Even if we assume that "setting your watch back 6 hours" means that the difference in longitude between the two points is exactly 90°, the question still doesn't specify the latitude of the two cities. And, of course, to get from a question where all the givens are time to an answer with the dimension of length, we would need to know the (ground) speed of the plane too.
To see concretely how there is too little information, Some other possible scenarios with a plane that flies with the same ground speed (and on the same earth) would be:

You fly from Frankfurt am Main to Santiago de Chile. It takes 15 hours, and when you arrive you set your watch back 6 hours.

or

You fly from Stockholm to Lagos. It takes 8 hours, and when you arrive you set your watch back 1 hour.

or even

You fly from Nuuk to Comodoro Rivadavia. It takes 15 hours, and when you arrive you set your watch back 1 hour.

If the problem was solvable with the given information, there would need to be a method that gave the same radius of the earth when given the inputs $(8,6)$ as for $(15,6)$ and $(8,1)$ and $(15,1)$.
Distance sources.
A: To me the most straightforward way of seeing that this is unsolvable without further information is to analyse the units/dimensions (see dimensional analysis).
None of the given information contained a unit of distance. Hence, it must be impossible to calculate a distance from it.
Sometimes a distance is "hidden" in a compound unit (e.g. a speed in km/h or a fuel economy in miles per gallon) that can be "broken out" by using a second piece of information (in the previous examples, a time in hours or fuel consumption in gallons). But there's none of that here.
Since there's no information about scale here whatsoever, one can imagine in a galaxy far away, on a world the size of a pearl, the Microuniversity of Minicambridge asking the same question.
A: My guess is that the interviewer was not expecting to get an exact answer, but was looking to see how confident your friend was at making their own approximations and working using those. For example, here are two guestimates that, if correct, would provide the information that is needed as previous answers have pointed out:


*

*Chicago and England have similar climates so there's probably not too much difference in latitude. They aren't close to the equator and aren't close to the pole, so let's guess about halfway between. i.e. latitude of 45 degrees.

*I know that military jets go supersonic, but you're probably talking about a commercial jet here and they don't. Let's guess about half the speed of sound: i.e. about 150m/s


Note that these estimates are incredibly crude, but they're reasoned and would have given your friend something to do that the interviewer could have judged.
p.s. A good source to emulate for this sort of crude estimation is the xkcd What If? articles, which use guesses like these to insight into situations much further from normal human experience.
A: Estimate plan flies at 500knts.  Fly for 8 hours = 4000miles.  Clock back 6 hours, so I'm 1/4 of the way round the earth.  Therefore circumference of earth is 4x = 16,000miles at this lattitude.  London is 53' so call it 45' for argument sake, using pythag/trig this means circumference is 0.7 (approx) of that at equator.  Therefore 16000/0.7 = 23,000 (approx.)  (actual is around 21,600 Nautical miles so not bad for an estimate)
A: The goal of this interview question wasn't a mathematics answer.  It is really a question that is suppose to trigger you to ask more question.
The issues with which Cambridge was important, as with all sorts of pseudo distance units being thrown at you.  The interviewee is suppose to be asking all sorts of questions to clarify and request more data.  This is very typical in standard business interactions, where clients always think they want something, but actually rarely does, and really has no idea what they want.
