We show that for any integer $n \geq 1$ and real $\varepsilon > 0$, the union of $n$ arithmetic progressions with pairwise distinct differences, each of length $n$, contains at least $c(\varepsilon)n^{2-\varepsilon}$ elements, where $c(\varepsilon)$ is a positive constant depending only on $\varepsilon$. This estimate is sharp in the sense that the assertion becomes invalid for $\varepsilon=0$. We also obtain estimates for the “asymmetric case" where the number of progressions is distinct from their lengths. (A corrected PDF is attached.)