International Mathematical Olympiad 1990 Problem 4

Let $\mathbb{Q}^+$ be the set of positive rational numbers. Construct a function $f: \mathbb{Q}^+ \to \mathbb{Q}^+$ such that

$$f(xf(y)) = \frac{f(x)}{y}$$

for all $x, y$ in $\mathbb{Q}^+$.