Question

Calculate how many liters (and gallons) of water are wasted in 1 month by a toilet that leaks 2 drops of water per second. (1 liter of water equals about 3,500 drops and 1 liter equals 0.265 gallon.)

Short answer

Approximately 1480.57 liters or 392.34 gallons are wasted in a month.

Step-by-step solution

Calculate Drops per Day

First, we need to find out how many drops are wasted each day. Since the toilet leaks 2 drops per second, in one minute (60 seconds), the toilet will leak: \[ 2 ext{ drops/second} imes 60 ext{ seconds/minute} = 120 ext{ drops/minute} \]In one hour (60 minutes), the toilet will leak:\[ 120 ext{ drops/minute} imes 60 ext{ minutes/hour} = 7200 ext{ drops/hour} \]In one day (24 hours), the toilet will leak:\[ 7200 ext{ drops/hour} imes 24 ext{ hours/day} = 172800 ext{ drops/day} \]

Calculate Drops per Month

Now, we calculate how many drops are leaked in one month. Assuming the month has 30 days, the toilet will leak:\[ 172800 ext{ drops/day} imes 30 ext{ days/month} = 5184000 ext{ drops/month} \]

Convert Drops to Liters

We know that 1 liter equals approximately 3500 drops. So, to find out how many liters are wasted in a month:\[ \frac{5184000 ext{ drops/month}}{3500 ext{ drops/liter}} \approx 1480.57 ext{ liters/month} \]

Convert Liters to Gallons

Finally, convert the liters to gallons. Since 1 liter equals 0.265 gallon:\[ 1480.57 ext{ liters/month} \times 0.265 ext{ gallon/liter} \approx 392.34 ext{ gallons/month} \]

Key concepts

Leakage Calculation

When calculating the leakage of water from a toilet, precision is key to understanding water waste. A simple leakage of 2 drops per second might seem trivial, but when you multiply these drops by the number of seconds in a day, the reality becomes significant. To calculate daily leakage:
- Multiply the rate of leakage by the number of seconds in a minute, then by minutes in an hour, and finally by hours in a day.
- For example, 2 drops per second become 120 drops per minute, 7200 drops per hour, and 172,800 drops per day.
Continuing this calculation over a month (30 days), we arrive at a surprisingly large number of drops: 5,184,000 drops. Understanding and performing these calculations is crucial to grasp the scale of potential water wastage.

Unit Conversion

Unit conversion is an essential skill in understanding and communicating the magnitude of water wastage. In this exercise, we convert the volume of water wasted from drops to liters and then to gallons.
- First, establish a relationship: 1 liter is approximately 3500 drops.
- Convert drops to liters by dividing the total number of drops by this conversion factor. For instance, 5,184,000 drops roughly equals 1,480.57 liters.
- Next, convert liters to gallons, knowing that 1 liter is 0.265 gallons. Multiply liters by this factor to get approximately 392.34 gallons per month.
Mastering these conversions helps quantify water wastage in familiar units, making the data more relatable and actionable.

Environmental Impact

Every drop of wasted water contributes to a larger environmental issue. Water conservation is essential to preserving resources and minimizing our environmental footprint. A leakage of 1480.57 liters or 392.34 gallons in a month is significant.
- This wastage drives home the importance of addressing even small leaks as they accumulate over time.
- Consider larger-scale implications: Increased water demand puts pressure on local water supplies and treatment facilities.
- Wasted water also leads to wasted energy, as significant resources are used to treat and pump freshwater.
Reducing leaks is an actionable step toward greater water conservation, positively impacting both local ecosystems and global water consumption.

Mathematical Problem Solving

Solving problems like calculating water wastage involves a series of mathematical steps that build on each other. This process hones students' abilities to manage real-world problems with multiple steps.
- Begin by identifying the problem — in this case, determining the total water wasted from a leak.
- Use basic arithmetic to complete calculations, increasing complexity by converting units.
- Ensure understanding by checking each part of the calculation. This helps verify accuracy and results in a stronger overall problem-solving capability.
Engaging in exercises like these strengthens analytical and critical thinking skills, essential components for academic success and personal resource management.