Fun with swimming numbers

We’ve had a couple of serious blog posts recently, so we thought we’d lighten the mood and have some fun with swimming numbers.
Imagine we have two swimmers: Tom and Richard. They are Facebook friends but live at opposite ends of the country and so don’t swim against each other. They are having an argument about who is the fastest swimmer, which would normally be easy to solve but Richard swims in a pool that is 10% longer than the standard 25m – it is 27.5m long.
Still, the two decide the can resolve their argument by each swimming four lengths of their respective pools as fast as they can, and then scaling their times accordingly. Tom subsequently swims 100m in 60s while Richard swims 110m in 66.5s.
“Case closed,” says Tom. “10% of my time is 6 seconds, therefore it would take me 66s to swim four lengths of your pool. I’m the fastest.”
“Wait a minute,” says Richard. “10% of my time is 6.65s. If you subtract that from 66.5, you get 59.85s. That means I’m faster.”
They argue about this for some time until their mutual friend Harry points out the flaw in Richard’s logic. He explains that while Richard has swum 10% more than Tom, Tom has swum 9.1% less than Richard (since 10/110 = 0.091). So Richard’s time should be reduced by 9.1% (6.045s) to 60.45 not 10%. It’s the same reason that if your house price rises by 10% and then drops by 10% you end up worse off. Percentages are tricky.
So, it now looks as if Tom is definitely the faster swimmer, but Harry is not so sure.
“The short course 100m freestyle world record is 44.94 and the 200m long course record is 1:42.00. This is twice the short course record plus 13.48%,” says Harry, while explaining he compared the short and long course records because both involve the same number of turns. “This means that for each additional 10m, a swimmer will slow down by about 1.35%.”
Harry therefore says to make the comparison, Tom’s time should be increased by 11.35% not 10%, which would give him a total time of 66.81 – three tenths of a second slower than Richard!
So who’s the fastest swimmer? We probably need to put these two in a head to head race to find out, but it does show that small changes in swimming (in this case just adding 2.5m to the length of a pool) can make big differences. Also, if you do swim in pools of different lengths, it’s probably not worth worrying too much about how your times compare.
Luckily most of this will be of little concern to open water swimmers, which is perhaps another of the sport’s attractions.
In case you’re wondering where this comes from, I quite often swim at the lovely Hampton Lido, which is 36m long (and heated) and was trying to figure out why my swim times didn’t scale as I expected.