Triangles $QPR$ and $RPS$ are similar. So:$\frac{PR}{PS}=\frac{PQ}{PR}$. Hence $PR^2=PQ\times PS=\frac{7}{3}\times\frac{48}{7}=16$.

So $PR$ is $4$ units long.

*This problem is taken from the UKMT Mathematical Challenges.*

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