A particle moves west at a speed of $25km/hr$ from the origin when $t=0$. Another particle moves north at a speed $20km/hr$ and stops at the origin when $t=1$, where $t$ is in hours. What will the minimum distance be between the $2$ particles and at what time $t$ does such minimum occur.

I have studied these questions for a while but i need help deriving an equation relating the two particle's movements to minimize them. Thanks for any help.

Note: The particles are co-planar.