Let t be the time driving at 40 mph (rocky area), in hours.


Then the time driving at 80 mph is (2-t) hours.


The total traveled distance is 40t + 80*(2-t).


Since it is 150 kilometers, in total, you have this equation


    40t + 80*(2-t) = 150.


Simplify and solve for t


    40t + 160 - 80t = 150

   -40t             = 150 - 160

   -40t             = -10

      t             =  =  = 0.25.


ANSWER.   of an hour driving through the rocky area, or 15 minutes.