  In this short note, we prove the conjecture of Benjamini, Shinkar, and Tsur
on the acquaintance time $AC(G)$ of a random graph $G \in G(n,p)$. It is shown
that asymptotically almost surely $AC(G) = O(\log n / p)$ for $G \in G(n,p)$,
provided that $pn > (1+\epsilon) \log n$ for some $\epsilon > 0$ (slightly
above the threshold for connectivity). Moreover, we show a matching lower bound
for dense random graphs, which also implies that asymptotically almost surely
$K_n$ cannot be covered with $o(\log n / p)$ copies of a random graph $G \in
G(n,p)$, provided that $pn > n^{1/2+\epsilon}$ and $p < 1-\epsilon$ for some
$\epsilon>0$. We conclude the paper with a small improvement on the general
upper bound showing that for any $n$-vertex graph $G$, we have $AC(G) =
O(n^2/\log n)$.
