<p>Let me say first that I didn’t write this one. It’s not from an SAT either. It was from a workshop I went to a long time ago and I adapted it. And when I first worked on it, I did exactly what I discourage others from doing: I assigned variables to the distances and then plugged and chugged through the algebra. It works, but it takes too long. And when I saw the answer, I was annoyed.</p>
<p>I think that this problem illustrates the importance of “number awareness” although admittedly on a subtle level. The Xiggi’s third solution shows what I mean. But you have to have noticed that the 20 and 60 have the harmonic mean of 30 and very few will pick that up. Still, when you read an SAT problem, remember that there are no coincidences. Numbers are chosen by the writers for a reason.</p>