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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 [tex]\frac{2}{3}[/tex] of a liter of water every 2 hours. If [tex]w[/tex] represents the amount of water lost and [tex]h[/tex] represents the number of hours, which equation represents this proportional relationship?

A. [tex]w = 3h[/tex]

B. [tex]w = \frac{1}{3}h[/tex]

C. [tex]h = \frac{1}{3}w[/tex]

D. [tex]\frac{2}{3}w = 2h[/tex]



Answer :

GinnyAnswer
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]

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