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:

7days1week×24hours1day×60minutes1hour×60seconds1minute×1drop2seconds×1liter5,750drops≈53L1week\frac{7 days}{1 week}\times \frac{24 hours}{1 day}\times \frac{60 minutes}{1 hour}\times \frac{60 seconds}{1 minute}\times \frac{1 drop}{2 seconds}\times \frac{1 liter}{5,750 drops}\approx \frac{53L}{1 week}

For one thirty-day month:

30days1month×24hours1day×60minutes1hour×60seconds1minute×1drop2seconds×1liter5,750drops≈225L1month\frac{30days}{1 month}\times \frac{24 hours}{1 day}\times \frac{60 minutes}{1 hour}\times \frac{60 seconds}{1 minute}\times \frac{1 drop}{2 seconds}\times \frac{1 liter}{5,750 drops}\approx \frac{225L}{1 month}

For one normal year:

365days1year×24hours1day×60minutes1hour×60seconds1minute×1drop2seconds×1liter5,750drops≈2,742L1year\frac{365 days}{1 year}\times \frac{24 hours}{1 day}\times \frac{60 minutes}{1 hour}\times \frac{60 seconds}{1 minute}\times \frac{1 drop}{2 seconds}\times \frac{1 liter}{5,750 drops}\approx \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?)