A lifeguard is stationed at point $A(0,7\mathrm{.}5m)$ on the beach, and a distressed swimmer is located at point $B(20m,-7\mathrm{.}5m)$ in the sea. The shoreline is represented by the x $-$axis, with the beach being above the x $-$axis $)>(0$ and the sea below the x $-$axis

The lifeguard runs on the beach at a speed of $5\frac{m}{s},$ and the lifeguard swims in the sea at a speed of $2\frac{m}{s}.$ The lifeguard's task is to reach the swimmer in the shortest possible time. The lifeguard can choose a point $P(x,0)$ on the shoreline to transition from running to swimming.

$1.)$ Determine the optimal point $P(x,0)$ on the shoreline such that the total rescue time is minimized.

$2.)$ Determine the rescue time.