Fallacy?

 1. If water truck carries water and food truck carries food, then fire truck carries fire.

2. Water truck carries water and food truck carries food.

3. Therefore, fire truck carries fire.

I don't see a logical fallacy there. Put another way :

If a is true AND b is true, then c is true
a is true AND b is true, THEREFORE c is true

The only question might be the possible meaningless clause of "fire truck carries fire", but that does not affect the logic flow.

I think I recall hearing this as a joke when I was six. 

A good logic test is given by Lewis Carrol in his book “Symbolic Logic” which states that "if we can think of any condition that would make the logical inference invalid, then it is an invalid logical inference". This fails the Lewis Carrol test.

P1) If P is true and Q is true, then R is true

P2) P is true and Q is also true

C) R is true

Since P and Q are both true, and the truth of this conjunction implies R, then R must also be true as Jim points out. The argument is formally valid.

However...since fire trucks do not carry fire, the major premise is unsound. So the argument is unpersuasive.

Not sure if their is a logic fallacy here. At most it would be Redefinition Fallacy

affirming the consequent .

1)If a truck carries something, then we can call it "something-truck".
2)"Fire-truck" is "something-truck".
3)Therefore it is a truck that carries fire. (WRONG)

A fire truck is just a truck related to fire (the relation is that it does not carry fire, it is used to extinguish fire).