# The Upside Down Swimming Calculation

## How two wrongs made a right.

17 October 2019

A few months ago I was sitting by a swimming pool in Las Vegas (as you do), reading a book, when a man and his young teenage son entered the water.

As the photo shows, at the edge of the pool there was a sign indicating the depth of the water, in imperial units (for the Americans) and metric (for the tourists). The dad spotted it and saw a chance for a bit of math(s) coaching.

The conversation went like this:

Dad (not seeing the decimal point*): Hey Joel, 5 feet is 15 metres, so how many feet in a metre?

Son: 15 divided by 5....that's three!

Dad: Yes, well done!

And the son was right - there are indeed roughly three feet in a metre (a metre is actually 3ft 3in). Yet both he and his dad had made a mistake.

In the USA, there's very little use of metric units, but even so it's a bit alarming that the dad was clearly unfamiliar with how huge 15 metres is. Meanwhile the son divided 15 by 5 instead of the correct, but harder, 5 divided by 15.

The reason why two wrongs made a (nearly) right is that the calculation 5 / 1.5 had been changed to 15 / 5 (i.e. the top of the fraction had been multiplied by 3, and the bottom by a bit more than 3).

* A few minutes later, the dad looked at the sign again and spotted that it said 1.5m not 15m. There was much confusion, and as far as I know they never got to the bottom of the problem.