## 1470.53 – Dripping Faucet

The faucet in a kitchen sink drips one drop every two seconds. If it takes 575 drops of water to fill a 100mL bottle, how many liters of water are being wasted in a week? How many are being wasted in a thirty-day month? How many in a normal year? Give all your answers to the nearest liter.

## Solution

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:

$\frac{7 days}{1 week}×\frac{24 hours}{1 day}×\frac{60 minutes}{1 hour}×\frac{60 seconds}{1 minute}×\frac{1 drop}{2 seconds}×\frac{1 liter}{5,750 drops}≈\frac{53L}{1 week}$

For one thirty-day month:

$\frac{30days}{1 month}×\frac{24 hours}{1 day}×\frac{60 minutes}{1 hour}×\frac{60 seconds}{1 minute}×\frac{1 drop}{2 seconds}×\frac{1 liter}{5,750 drops}≈\frac{225L}{1 month}$

For one normal year:

$\frac{365 days}{1 year}×\frac{24 hours}{1 day}×\frac{60 minutes}{1 hour}×\frac{60 seconds}{1 minute}×\frac{1 drop}{2 seconds}×\frac{1 liter}{5,750 drops}≈\frac{2,742L}{1 year}$

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?)