Minimize Time Optimization Algorithm

Hi,

From our home at

(0, 0), we go to point (10, 10) taking minimal time. There are three land. The area

A= {(x, y) : 2< x < 6, y ∈ R} where we can move with speed of 2 km/h.

Then, second area is

B = {(x, y) : 6≤ x ≤ 8, y ∈ R}

in secon area speed at 1 km/h. All other area is C, where we can proceed at 8 km/h.

Formalize the underlying optimization problem, variables and constraints, give a suitable objective function such as time. Which algorithm can I use?

Best regards.