Lilly is working on a classic math problem:

*A hot tub can be filled with one of two water faucets. The first alone would fill the tub in 2 hours and the second one alone would fill the tub in 4 hours. How long does it take to fill the tub with both of them turned on at the same time?*

Lilly thinks this problem is a little too easy and so starts to play around with different ways of solving it. Being a big fan of geometry, she draws a right triangle, with one leg being 2 and the other leg being 4 to represent the time for each faucet.

She then inscribes a square in the triangle so that two sides align with the legs and one corner lies on the hypotenuse:

Lilly then notices that the length of the side of the square is actually the solution to the problem!

- Is she right?
- Does this work for other numbers? (different times for the faucets to fill the tub)
- Does this work for all numbers?