Is walking faster than running for raising pets?

Raising a pet in Danganronpa 2 involves accumulating steps by either walking or running.

The egg hatches after 100 steps, the child (Chibimi) turns into a pupa after 1000 additional steps, which evolves into its adult form after another 100 steps. The adult form depends on how well one took care of the child. After 2000 more steps the adult lays an egg and leaves after giving a present.

In an effort to raise all sorts of different pets, I'd like to know the fastest way to accumulate steps: walking or running?

I know that running a given distance yields less steps than walking the same distance, but what about time? From what I could tell with my limited timing abilities, walking and running appeared to be equally fast.

Running is faster because the time of the run is greater than the time of walking.