A point $‘P’$ on a CNC controlled $XY$-stage is moved to another point $‘Q’$ using the coordinate system shown in the figure below and rapid positioning command $(G00)$
A pair of stepping motors with maximum speed of $800$ rpm, controlling both the $X$ and $Y$ motion of the stage, are directly coupled to a pair of lead screws, each with a uniform pitch of $0.5$ mm. The time needed to position the point $‘P’$ to the point $‘Q’$ is _________ minutes (round off to $2$ decimal places).
