USAMO 1979 Problem 4

$\mathrm{P}$ lies between the rays $\mathrm{OA}$ and $\mathrm{OB}$. Find $\mathrm{Q}$ on $\mathrm{OA}$ and $\mathrm{R}$ on $\mathrm{OB}$ collinear with $\mathrm{P}$ so that $1 / \mathrm{PQ}+1 / \mathrm{PR}$ is as large as possible.