The number of hours, h, it takes for a block of ice to melt varies inversely to the temperature, T, so long as the temperature is above 32º and the volume of the ice is constant. It takes 2 hours for a chunk of ice to melt at 60°. How long will it take the ice with the same volume to melt at 40°?
A. 5
B. 1.5
C. 3
D.4

If two variables are directly proportional to one another, it indicates that when one doubles in size, the other does as well; if one triples, the other does as well; and if one half, the other does as well.

Given that the time needed for an ice block to melt is inversely proportional to the temperature. Therefore, the reaction can be written as,

[tex]\rm Time \propto \dfrac1{Temperature}[/tex]

Now, to remove the proportionality symbol it is needed to introduce a constant, therefore, we can write,

[tex]\rm Time = \dfrac k{Temperature}[/tex]

Given that it takes 2 hours for the ice to melt at 60°. Therefore, the value of k can be written as,

[tex]\rm 2= \dfrac k{60^o}\\\\k = 120[/tex]

Now, the time it takes for the ice to melt at 40° can be written as,

[tex]\rm Time = \dfrac{120}{Temperature}\\\\Time = \dfrac{120}{40^o} = 3\ hours[/tex]

Hence, the time needed for the ice to melt at 40° is 3 hours.

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