Running around a track at different speeds problem

Question

Squirrels run around a track in both directions. A dog runs round the track 3 times faster than the average squirrel, what is the ratio of the squirrels the dog expect to overtake compared to those it passes on-coming?

I have no idea how to tackle this, any help would be great.

Answer 1

My assumption is that this is meant to be 'clever' and not really mathematical, i.e. 100% since all of the squirrels will be running away from the dog.

If that isn't the case, there isn't nearly enough information to start answering that question. What proportion of squirrels run in the same direction as the dog? Do any of them change direction? What time frame are we looking at, and what is the distribution of squirrels on the track? etc etc

Answer 2

We need to make some assumptions to be able to answer this question. The biggest assumptions are that there are as many squirrels running in one direction as in the other, and that the squirrels are not affected by the presence of the dog. I'll also assume that we are looking at a long enough time span that the distribution of the squirrels around the track doesn't matter - any bunching of the squirrels is averaged out in the long run.

In that case you can just simplify it to have two squirrels, one in each direction, and look at what happens when they run a single lap of the track, while the dog runs three laps. If there were more squirrels, you can just match them up in opposite travelling pairs, and each pair will give the same answer.