To determine the equation representing the relationship between the amount of water lost [tex]\( w \)[/tex] and the number of hours [tex]\( h \)[/tex], we need to carefully analyze the given data.
Given:
- The leak releases [tex]\(\frac{2}{3}\)[/tex] of a liter of water every 2 hours.
First, we need to find the rate at which the water is leaking per hour. To do this, we can divide the amount of water lost by the number of hours.
[tex]\[
\text{Water lost per hour} = \frac{\frac{2}{3} \text{ liter}}{2 \text{ hours}} = \frac{2}{3} \div 2 = \frac{2}{3} \times \frac{1}{2} = \frac{2}{6} = \frac{1}{3} \text{ liters per hour}
\][/tex]
Now, we know that the water is leaking at a rate of [tex]\(\frac{1}{3}\)[/tex] liters per hour.
To express the total amount of water lost [tex]\( w \)[/tex] in terms of the number of hours [tex]\( h \)[/tex]:
[tex]\[
w = \left(\frac{1}{3} \text{ liters per hour}\right) \times h \text{ hours}
\][/tex]
So the equation representing the proportional relationship between the amount of water lost and the number of hours is:
[tex]\[
w = \frac{1}{3}h
\][/tex]
Therefore, the correct answer is:
B. [tex]\( w = \frac{1}{3}h \)[/tex]
