At what education level is this "simple" problem adequate?

Question

Given the following problem:

Alice, Bob and Carl stand on a straight line.
Alice is one rod away from Bob.
Dana stands one rod away from both Bob and Carl.
Carl is as far from Alice as Alice is from Dana.

How far can Alice be from Carl?

Answer using a well-formed sentence, with any distance expressed (in rod) with three significant digits (calculators allowed).

Question: At what education level could we expect that more than one in ten students give a mathematically correct answer, in exam conditions?

Note: I authored this problem, and know its solution.

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Update: Spoiler with reference answer to the original problem follows; hover mouse to see it.

Alice is either 1.62… or 0.618… rod away from Carl.

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Update: Some have trouble with the problem's wording (which is an important aspect of the question), so here is a restatement in geometry terms; hover mouse to see it.

$A$, $B$, $C$, $D$ are distinct points, with $A$, $B$, $C$ collinear,
such that $|AB|=|BD|=|CD|=1$ and $|AC|=|AD|$.

Give the set of possible $|AC|$ rounded to 3 significant digits.

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Update: link to spoiler illustration; ctrl-click for new window or tab.

Answer 1

To be able to solve the problem I think a student would need to know

• basic algebra
• some trigonometry
• some geometry, including the concept of circles, triangles, and equidistance

At what education level...

Education level is a strange concept, but I think a bright student in an advanced secondary mathematics class should be able to solve this. It's somewhat tricky but it's not exceedingly difficult.

It's definitely well beyond the primary / elementary school student, and below the university / college level mathematics student. Probably above the level of the general high school mathematics student but within grasp of the advanced high school student.

Just my opinion, of course.

Answer 2

I might be being silly but it appears to me that the question is not written very well and it is mathematically inaccurate.

My main issue is that Dana might not be able to stand anywhere. How do we know that there is a place that is one rod away from both Bob and Carl? They might be at a distance of more than two rods away from each other, in which case there is no possible place for Dana to stand at all!