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

Approximately 1,480 liters or 392 gallons of water are lost, filling around 9 bathtubs.

Step-by-step solution

Convert Drops to Liters per Second

First, we know the leak rate is 2 drops per second. Given that 1 liter equals 3,500 drops, the rate in liters per second is calculated as follows:\[ \text{liters per second} = \frac{2 \text{ drops}}{3500 \text{ drops per liter}} = \frac{2}{3500} \text{ liters per second}. \]

Calculate Liters per Month

Next, we convert the leak rate to a monthly rate. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and about 30 days in a month. Thus, the total number of seconds in a month is:\[ 60 \times 60 \times 24 \times 30 = 2,592,000 \text{ seconds.} \]Now we calculate the total volume in liters:\[ \frac{2}{3500} \times 2,592,000 = \frac{2 \times 2,592,000}{3500} \approx 1,480 \text{ liters.} \]

Convert Liters to Gallons

Using the conversion factor 1 liter = 0.265 gallon, we find:\[ 1,480 \text{ liters} \times 0.265 \text{ gallons per liter} \approx 392 \text{ gallons.} \]

Calculate Number of Bathtubs

Each bathtub holds about 151 liters or 40 gallons. To find out how many bathtubs could be filled:For liters: \[ \frac{1,480 \text{ liters}}{151 \text{ liters per bathtub}} \approx 9.80. \]For gallons:\[ \frac{392 \text{ gallons}}{40 \text{ gallons per bathtub}} \approx 9.80. \]Thus, approximately 9 full bathtubs could be filled with the lost water.

Key concepts

Understanding Unit Conversion

Unit conversion helps us convert quantities from one form of measurement to another. In this exercise, we convert water’s flow from drops to liters, then from liters to gallons. First, understand the basic conversion: 1 liter equals 3,500 drops. So, if a faucet leaks 2 drops per second, we can determine the flow rate in liters per second by dividing the number of drops by the conversion factor. Hence, the leak is \(\frac{2}{3500}\) liters per second.
This concept is crucial in many areas such as cooking, science, and even daily activities, because:

• It allows for precise measurements.
• It helps compare different quantities easily.
• It is essential for standardizing measurements globally.

Learning unit conversion is fundamental in enhancing comprehension especially when dealing with different measurement units across various systems.

The Importance of Water Conservation

Water conservation is about reducing wastage and using water efficiently. This exercise demonstrates the impact of even a tiny leak. Losing water at 2 drops per second might seem insignificant, but when accumulated over a month, it results in about 1,480 liters lost.
Water is a critical resource, and its scarcity affects life globally. By understanding water conservation:

• We realize the importance of fixing even minor leaks.
• We learn to appreciate resource management.
• We acknowledge the preciousness of water and the need to safeguard it for the future.

This lesson encourages mindful usage and the significance of maintaining systems to prevent loss.

Applying Mathematics in Real-life Situations

Math helps provide solutions to real-world problems, including efficiency in resource management. By calculating the effects of a water leak, we apply mathematical principles practically.
First, we calculated the monthly water loss in liters and then converted it to gallons. Understanding these computations:

• Gives insight into the sizeable impact of small, ongoing losses.
• Enables us to quantify resources lost, furthering conscious decision-making.
• Prepares us to tackle similar issues pragmatically across different scenarios.

This exercise underscores the utility and applicability of mathematics beyond the classroom, making understanding math relevant to everyday life.