TheDoctorWhoNut
I don't get the last bit.
Since the mathematican has in effect 'solved' the first fire, he makes the second one the same, so it is 'solved as well', but you don't have to do the same working out as well.
A (possibly) helpful analogy:
Say the first fire represents 2x = 4
Putting out the fire is in effect working out x = 2
With the last bit, the scenario represents 2x + 2 = 6
My moving the bucket, it becomes 2x = 4
i.e. the mathematician makes the second problem one has has already solved, so he knows the answer from that.
See!? By explaining the joke, I have just removed what little humerous merit it contained.