## 2010 Galois Contest

I took the Galois contest this morning, it was a 75 minute test, with calculators allowed. It has four questions, each worth ten points, and a full written response is required.

I’m going to post my answers here. These are my own answers, so no guarantee that they’re correct.

Although some schools haven’t took it yet, it should still be fine. Nobody would care if I leak answers. Yay me. Anyways, first question.

### Problem 1

1. Emily has an old showerhead using 18L of water per minute and a new showerhead using 13L a minute.

a) How long does it take to use 260L of water using the new showerhead?

13L per minute and 260L of water, so 20 minutes.

b) How much less water is used in 10 minutes with the new showerhead than the old one?

In 10 minutes the old showerhead uses 180L of water and the new one only 130L.

So the new one uses 50L less water.

c) Water costs 8 cents per 100L. How much money is saved by using the new showerhead instead of the old one, in a 15 minute shower?

In 15 minutes the old showerhead uses 270L of water and the new one uses 195. So the difference is 75L which costs 6 cents.

d) How long (in minutes) does it take to save $30 by using the new showerhead? If m is the time showered in minutes then the cost of the old shower per minute (in cents) is $0.08 \cdot 18m$ or $1.44m$ and the new shower $0.08 \cdot 13m$ or $1.04m$, and so the difference is $0.4m$. If we save$30 then we save 3000 cents, and $0.4m = 3000$ and m = 7500 minutes.