Question
Select the correct answer. Luke has a situation on his hands. A pipe in his house froze and cracked from cold weather. Now he has a water leak. The leak has been releasing \( \frac{2}{3} \) of a liter of water every 2 hours. If \( w \) represents the amount of water lost and \( h \) represents the number of hours, which equation represents this proportional relationship? A. \( w=3 h \) - B. \( w=\frac{1}{3} h \) C. \( h=\frac{1}{3} w \) D. \( \frac{2}{3} w=2 h \)
Ask by Ball Mccarthy. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( w = \frac{1}{3} h \)
Solution
To determine the correct equation representing the proportional relationship between the amount of water lost (\( w \)) and the number of hours (\( h \)), let's analyze the given information:
- **Rate of Leak:** \( \frac{2}{3} \) liters every 2 hours.
First, find the rate of water loss per hour:
\[
\text{Rate} = \frac{\frac{2}{3} \text{ liters}}{2 \text{ hours}} = \frac{1}{3} \text{ liters per hour}
\]
This means that for every hour that passes, \( \frac{1}{3} \) liters of water are lost. Therefore, the amount of water lost (\( w \)) is directly proportional to the number of hours (\( h \)):
\[
w = \frac{1}{3}h
\]
**Answer:**
**B. \( w = \frac{1}{3} h \)**
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Simplify this solution Beyond the Answer
To solve this problem, let's focus on the leak. If \( \frac{2}{3} \) of a liter is lost every 2 hours, we can determine the amount lost per hour, which is \( \frac{1}{3} \) of a liter. Thus, the relationship can be expressed as \( w = \frac{1}{3} h \), where \( w \) is the total amount of water lost and \( h \) is the total number of hours the leak has been happening. Therefore, the correct answer is B. Are you ready to fix that leak with some elbow grease? You might want to grab a space heater, some insulation, and maybe a towel or two, just to be safe! Keeping those pipes warm and snug can stop the freeze before it starts.
