increasing the speed of an object blank its potential energy

There is no direct connection between the speed of an object and its potential energy.  

UNLESS the object is falling, and it's GETTING its speed FROM its potential energy.  If that's what's going on, then of course if the speed increases, the object's kinetic energy increases, and that increase has to come from using up some of the potential energy.

b. latent learning (the word "latent" itself means something that exists but isn't obvious, only under certain conditions! )

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)