Well, if three cats catch three mice in three minutes then it means that, on an average, they catch one mouse per minute. If in one minute they catch one mouse, then in 100 minutes they will catch 100 mice. So, to catch 100 mice in 100 minutes, these three cats will suffice!
I don't know from where they can catch 100 mice; and having caught them how can three cats feed on 100 mice? Anyway, that is their problem not mine.
By the way when I started working on the riddle I presumed that the cats were individualists who liked to go about their own ways rather than work as a team. Under that premise I reached the conclusion that it takes one cat three minutes to catch one mouse. That's right isn't it? Say, for instance, the cats start on their killing spree at 11 am, then the first cat catches its mouse by 11:03; the second cat catches its mouse during the same period, and so does the third. So we have three cats catching three mice in three minutes.
If a cat catches a mouse in three minutes then in 100 minutes it will catch 100/3, or 33.3333333....., mice. I don't know how it can catch 33.333333... mice but that is what my math leads me to conclude. I think I was along the right track if you are willing to ignore the recurring decimal mouse. Thus, if one cat catches 33.333333.... mice in 100 minutes, then three cats will be required to catch 3 x 33.333333.... = 99.99999..... mice in 100 minutes. But 99.99999..... is equal to 100. So I arrive at the same answer. If only I had exhibited a little more patience I could have got the hot dog!
By the way, don't you agree that 99.999999.... is equal to 100? Of course it is. Let me prove it.
Consider the following sum: 100/3 + 100/3 + 100/3.
Now, 100/3 + 100/3 + 100/3 = 300/3 = 100.
But 100/3 = 33.333333.....
Thus, 33.33333...... + 33.33333333....+ 33.333333..... = 100, or 99.9999..... = 100.