  The entanglement of purification $E_P(A\colon B)$ is a powerful correlation
measure, but it is notoriously difficult to compute because it involves an
optimization over all possible purifications. In this paper, we prove a new
inequality: $E_P(A\colon B)\geq \frac{1}{2}S_R^{(2)}(A\colon B)$, where
$S_R^{(n)}(A\colon B)$ is the Renyi reflected entropy. Using this, we compute
$E_P(A\colon B)$ for a large class of random tensor networks at large bond
dimension and show that it is equal to the entanglement wedge cross section
$EW(A\colon B)$, proving a previous conjecture motivated from AdS/CFT.
