One Fault In Nine Thousand

A service's working set has grown past physical memory. A page comes back from NVMe swap in 90 microseconds; an access that hits memory costs 100 nanoseconds. Model the average access time as

$\text{AAT} = T_M + p \cdot T_D$

where $p$ is the page fault rate, $T_M = 100\ \text{ns}$ and $T_D = 90{,}000\ \text{ns}$.

What is the largest fault rate that keeps average access time within 10 percent of the no-fault case?