So there is a mind (one that asks this question) and there is the body (fingers typing this question of the mind). This is not "I" or "me". So when the body goes running and when the mind or brain is thinking, why does it get tired? Or is it just the illusion of tired?
It is you who gets hungry. The problem start when you mentally identify that "I am hungry". If you just let be as another sensation without metal conceiving in relation to I there is no problem and pain will be reduce and stress from the situation non existent. Many metal construction or notion or perception of "I" or "mine" leads to misery. It is holding on to this metal construction or notion or perception of "I" or "mine" which should stop. As when this stops here is no identification or notion or perception or metal conceiving of a self in the person this is what is generally referred as no self or nonself, i.e., the person is devoid of holding on to any mental conceiving of a person hence does not have any sense as this is a person, or this is me, etc.
From a Madhyamika-Prasangika viewpoint, when I see your body, I see BlackFlam3. When I hear your voice, I hear BlackFlam3. When your body is unwell, you are sick. When anger arises in your mind, you are angry. Yet, your are neither your body nor your mind. You depend on them, though, for you would not be who you are if t was not for them. You even depends on what is not even in your continuum, such as external objects that you apprehend, and so forth.
As a person, you exist conventionally. That conventional object, the person, is an object apprehended by conventional cognizers. The person is seen, heard, touched, smelled, being remembered, and so forth. That person is an object of pride, anger, jealousy, desire, and so forth. Yet, that person which is loved, hated, seen... is not intrinsically one with any of its aggregates.
In the same way, I see your hand, but I do not see the whole of it (back and front and bones, and so forth) and your hand is not intrinsically what I see of it.
The problem is as follows: as soon as you engage into analysis, wandering whether the person is intrinsically one or intrinsically different from its aggregates, you engage in ultimate analysis. And what the mind of ultimate analysis finds (realizes) is the ultimate truth which is the absence of a truly existent person. So, of course, when you ask yourself "but am I that feeling? or this body? or am I my flesh? but if I was, I could not say 'my' as if there was an I possessing it, and so forth" you take the direction of ultimate analysis and you will not find the person.
Identifying the conventional objects as objects found by conventional valid cognizers (eye-consciousness, ear-consciousness and so forth, that do not engage into analysis) is of utmost importance. So, yes, conventionally, it is enought for me to see your body to see you.
Maybe of thinking in loops? May Mr/Mrs stay with that and do fall into the all is anatta nonsens, which is simply vibhava tanha. Mr/Mrs would get tired even faster.
(Note: this answer has not been given with the agreement to be means of trade or the purpose of/for trade and/or keep people trapped and bound. How you handle it lies in your sphere, but does not excuse the deed here either.)
So when the body goes running and when the mind or brain is thinking, why does it get tired? Or is it just the illusion of tired?
Perhaps further to Tenzin's saying that the mind-and-body is not "I", if you only ask, "Why does the body get tired?" then IMO an answer might be explained using (not Buddhism itself but using) physiology, biochemistry, maybe even thermodynamics.
It does reminds me of the Buddha's saying, though, "all compound things are subject to decay".
A slightly different question (maybe a question we should ask, instead) could be whether you're mindful, or what you're mindful of -- and, whether you find "it gets tired" dissatisfactory. Because maybe what's important to keep in mind is "dukkha" and "cessation of dukkha".