Meaning behind the equation x=1/4+x/4 for the average distance between two points on a line?
My colleague and I were discussing the average distance between two uniformly distributed points on a line segment of length 1 (which we know is 1/3). I solved it using the standard double integral method, which took me quite a while.
My colleague looked at my math and said he had a much easier way to think about it. He just wrote down this equation:x=1/4+x/4
Which, of course, solves to x = 1/3.
He told me I should spend some time trying to figure out the concept behind the equation on my own, rather than just running to an AI for the answer. So I try feeding the equation into an AI tool anyway, but it just gave me complex explanation that I couldn't really wrap my head around.
Can someone explain the meaning behind his equation in a simpler, more intuitive way?