Question

Calculate how many liters (and gallons) of water are lost in 1 month by a toilet or faucet that leaks 2 drops of water per second. (One liter of water equals about 3,500 drops and 1 liter equals 0.265 gallon.) How many bathtubs (each containing about 151 liters or 40 gallons) could be filled with this lost water?

Short answer

About 1,480.34 liters (392.29 gallons) are lost, filling approximately 9 bathtubs.

Step-by-step solution

Calculate Drops per Month

First, calculate the number of seconds in a month. Assume there are 30 days in a month. There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute. Therefore, the total number of seconds in a month is:\[30 \times 24 \times 60 \times 60 = 2,592,000 \text{ seconds}\]If the faucet leaks 2 drops per second, then the total number of drops leaked in a month is:\[2 \text{ drops/second} \times 2,592,000 \text{ seconds} = 5,184,000 \text{ drops}\]

Convert Drops to Liters

Knowing that 1 liter equals about 3,500 drops, convert the total number of drops to liters:\[\text{Liters} = \frac{5,184,000 \text{ drops}}{3,500 \text{ drops/liter}} \approx 1,480.34 \text{ liters}\]

Convert Liters to Gallons

With 1 liter equating to approximately 0.265 gallons, find out how many gallons the leaked water equals:\[\text{Gallons} = 1,480.34 \text{ liters} \times 0.265 \text{ gallons/liter} \approx 392.29 \text{ gallons}\]

Calculate Number of Bathtubs Filled

Each bathtub holds about 151 liters or 40 gallons. Using the leaked water amount in liters:\[\text{Number of Bathtubs} = \frac{1,480.34 \text{ liters}}{151 \text{ liters/bathtub}} \approx 9.80\]The number of bathtubs that can be filled with the leaked water is approximately 9 if considering just whole bathtubs.

Key concepts

Water Leakage

Water leakage represents a persistent yet often overlooked issue in water conservation. When devices such as faucets or toilets have even a small leak, they can contribute to significant water loss over time. Consider a faucet that drips only 2 drops per second. While this may seem trivial, in the span of a month, it adds up to millions of drops. This type of leakage is a common problem and can lead to high water bills and increased strain on local water resources.

To prevent unnecessary water wastage and to protect our environment, it is essential to routinely check and repair leaks in household plumbing fixtures. Simple actions like this can lead to substantial savings and contribute to water conservation efforts globally.

Regular monitoring, maintenance, and immediate fixing are key steps that can help in reducing the widespread problem of water leakage.

Leak Rate Calculation

Leak rate calculations allow us to quantify the amount of water lost through leaks over a specific time period. In the case mentioned, we determine the total number of drops leaked in one month. First, we calculate the seconds in a month, considering an average of 30 days:

• Seconds in a month: 30 days × 24 hours/day × 60 minutes/hour × 60 seconds/minute = 2,592,000 seconds.

If a faucet leaks 2 drops per second, we can calculate the total drops:

• Total drops leaked = 2 drops/second × 2,592,000 seconds = 5,184,000 drops

This calculation is crucial for understanding the overall impact of small leaks when not addressed timely, thus emphasizing the importance of promptly addressing any leaks in infrastructure.

Unit Conversion

Unit conversion plays a pivotal role in interpreting leak data into usable metrics. For our calculation, we need to know how many drops are equivalent to one liter and how liters convert into gallons. Given that one liter is approximately 3,500 drops:

• Liters = 5,184,000 drops ÷ 3,500 drops/liter ≈ 1,480.34 liters

Furthermore, to convert these liters into gallons, we use the fact that one liter is about 0.265 gallons:

• Gallons = 1,480.34 liters × 0.265 gallons/liter ≈ 392.29 gallons

Unit conversions like these are not only essential for solving exercises but are also valuable in real-life applications where different measurement systems need to be harmonized.

Environmental Impact

Understanding the environmental impact of water leakage is crucial. When examining the amount of water wasted, approximately 1,480.34 liters or 392.29 gallons in one month from a small leak, the environmental significance becomes apparent.

This wasted water could fill nearly 10 average bathtubs. The unintentional wastage of such large quantities of fresh water indicates a strain on water resources, which are already limited in many parts of the world. Moreover, excessive water leaks require more treatment and redistribution cycles, which also have environmental costs.

Promoting efficient water use, fixing leaks, and educating the public play crucial roles in mitigating these impacts. Through increased awareness and simple measures, significant positive changes can be made toward conserving our precious water resources.