  Consider the hypergraph bootstrap percolation process in which, given a fixed
$r$-uniform hypergraph $H$ and starting with a given hypergraph $G_0$, at each
step we add to $G_0$ all edges that create a new copy of $H$. We are interested
in maximising the number of steps that this process takes before it stabilises.
For the case where $H=K_{r+1}^{(r)}$ with $r\geq3$, we provide a new
construction for $G_0$ that shows that the number of steps of this process can
be of order $\Theta(n^r)$. This answers a recent question of Noel and
Ranganathan. To demonstrate that different running times can occur, we also
prove that, if $H$ is $K_4^{(3)}$ minus an edge, then the maximum possible
running time is $2n-\lfloor \log_2(n-2)\rfloor-6$. However, if $H$ is
$K_5^{(3)}$ minus an edge, then the process can run for $\Theta(n^3)$ steps.
