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11+ Questions: 5. Cats and Mice

17 August 2017

How long does it take a cat to catch a mouse? We try and find out in this week's pick of the 11+'s hardest maths questions.

It’s time for the next part of our series looking at some of the hardest 11+ maths questions in recent years, and this week we’re going to be looking at the mathematics of cats chasing mice. It’s another short one for this week but it’s quite a nice brain twister, so let’s have a look.

Question: 3 cats can catch 3 mice in 3 hours.

  1. How long would it take 3 cats to catch 1 mouse?
  2. How long would it take for 1 cat to catch 1 mouse?

This is a question about the rate at which something happens – at which cats catch mice – but we don’t need to use any particular formula to answer these questions; we only need to think logically.

Let’s take a look at the first question:

  1. How long would it take 3 cats to catch 1 mouse?

As the question stands we know that it takes 3 cats 3 hours to catch 3 mice. If there are 3 fewer mice (only 1 mouse) to catch, that means that our cats are doing 3 times less work. So it makes sense that they will be working for 3 times less. So the answer is that it will take our 3 cats 1 hour to catch one mouse.

Now we come on to question B. If we don’t keep our wits about us, we can very easily be distracted by the language of this question.

  1. How long would it take for 1 cat to catch 1 mouse?

It might seem to make sense that if it takes 3 cats 3 hours to catch 3 mice, it will take 1 hour for 1 cat to catch 1 mouse. That is, until you think about it.

There are two ways to think about this, and one is by using our answer to question A.

If it took 3 cats 1 hour to catch 1 mouse, that means that if we have 3 times fewer cats, it’s going to take 3 times longer for that 1 mouse to be caught!

Another way of approaching this question is like this: if we imagine the environment where the cats are chasing after the mice, we might imagine that there are 3 rooms. In each room there is a cat and a mouse. All 3 cats are catching all 3 mice simultaneously.

Now let’s remove one cat and its mouse from the environment. Do the other cats magically speed up? No, they still take 3 hours to catch their respective mice.

The same is true if we take away another cat and mouse. If there is only one cat and one mouse, the cat will still take 3 hours to catch the mouse.

And so there is our answer. It takes 1 cat three hours to catch 1 mouse.

Until next week!

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