1470.53 – Dripping Faucet

First, note that it takes 5,750 drops of water to make one liter.

To find how many liters are being wasted in a given amount of time, it helps to use dimensional analysis.

For one week:

$$\begin{align*}&\dfrac{7 \ \days}{1 \ \week} \times \dfrac{24 \ \hours}{1 \ \day} \times \dfrac{60 \ \minutes}{1 \ \hour}\\[1em]\times \ & \dfrac{60 \ \seconds}{1 \ \minute} \times \dfrac{1 \text{ drop}}{2 \ \seconds} \times \dfrac{1 \ \liter}{5,750 \text{ drops}} \\[0.5em]\hline \\[-1em]\approx \ & \dfrac{53 \ \liters}{1 \week}\end{align*}$$

For one thirty-day month:

$$\begin{align*}&\dfrac{30 \ \days}{1 \ \month} \times \dfrac{24 \ \hours}{1 \ \day} \times \dfrac{60 \ \minutes}{1 \ \hour}\\[1em]\times \ & \dfrac{60 \ \seconds}{1 \ \minute} \times \dfrac{1 \text{ drop}}{2 \ \seconds} \times \dfrac{1 \ \liter}{5,750 \text{ drops}} \\[0.5em]\hline \\[-1em]\approx \ & \dfrac{225 \ \liters}{1 \ \month}\end{align*}$$

For one normal year:

$$\begin{align*}&\dfrac{365 \ \days}{1 \ \year} \times \dfrac{24 \ \hours}{1 \ \day} \times \dfrac{60 \ \minutes}{1 \ \hour}\\[1em]\times \ & \dfrac{60 \ \seconds}{1 \ \minute} \times \dfrac{1 \text{ drop}}{2 \ \seconds} \times \dfrac{1 \ \liter}{5,750 \text{ drops}} \\[0.5em]\hline \\[-1em]\approx \ & \dfrac{2742\ \liters}{1 \ \year}\end{align*}$$

Maybe it’s time to call a plumber.

(Note: is it necessary to start from scratch each time? How can you use one result to get the next one?)