Why isn't a molecule's kinectic energy dependant on mass?

[aracali]

So my book say's

"A molecule's average translational kinetic energy depends only on the temperature, not on the molecule's mass. If two gases have the same temperature, their molecules have the same average translational kinetic energy."​

My question is, why?
I mean, wouldn't molecules with bigger mass have more inertia and therefore would travel slower with the same amount of energy (which is related to temperature)?

 

[A.T.]

I mean, wouldn't molecules with bigger mass have more inertia and therefore would travel slower with the same amount of energy (which is related to temperature)?

Yes.

 

[Karan Punjabi]

Yes.

Also from my point view if we consider two different gases and we supply same amount of heat to both of them the one gas whose atoms are more heavier will have less kinetic energy and one which is lighter than the other one will have more kinetic energy

 

[CWatters]

If heat is energy why would one gas end up with more than the other