?

In lesson 5.8 Tengo mucha hambre tenemos que comer algo. why would they not say , Tengo mucha hambre Tengo que comer algo.   seeing that if we eat something, that will not help his hunger at all.

In English it would make sense to say "I'm very hungry.  We have to eat something".  We state something we feel personally and then generalize it to the group.  In that lesson, they were just giving example of how to say such things.

Robert's explanation is correct and to the point. I would only add that one could also say,

Tengo mucha hambre. Tengo que comer algo.

I think that in this context the speaker is including whomever he is speaking to in his need to eat, assuming that they both (or all) need to eat, or just being polite and including the other(s) in his decision to eat. As Robert noted, this and the other sentences in the lesson are showing the use of different persons of the same verb.