Olympic speed and time

The Olympics have generated so many lovely numbers to use for mental mathematics! I was thinking yesterday, for example, about how I could easily relate how much faster one competitor runs than another to the difference in their times?

Say, runner B's average speed is x% faster than runner A's. How will their times for the event be related?

Now we have to be careful here, because percentage increases and decreases don't always behave as we think they should intuitively. For example, if P is 10% larger than Q it is NOT true to say that Q is 10% smaller than P: it's about 9.1% smaller.

So, I came up with this neat hypothesis:

If B's average speed is x% faster than A's, then A's time is x% greater than B's.

What do you think? Is this true? Try it with some easy numbers and see whether or not it works.

For example, if Another runs 100 metres at an  average speed of 10 metres per second, and Bolt's average speed is 5% greater than this ...