Question

The number of hours it takes for ice to melt varies inversely with the air temperature. A block of ice melts in 2.5 hours whenthe temperature is 54 degrees.How long would it take for the same block of ice to melt if the temperature was 45 degrees?

Answer 1

Let t be the time in hours it takes a block of ice to melt at T degrees.

Since both variables have an inverse relation, we can say that:

$t=\alpha\cdot\frac{1}{T}$

Where alpha is a constant value.

Since we know that a block of ice melts in 2.5 hours when the temperature is 54 degrees, we can plug in such data and find alpha as following:

$\begin{gathered} 2.5=\alpha\cdot\frac{1}{54}\rightarrow2.5\cdot54=\alpha \\ \Rightarrow\alpha=135 \end{gathered}$

Therefore, our expression would be:

$t=\frac{135}{T}$

For T = 45,

$\begin{gathered} t=\frac{135}{45} \\ \\ \Rightarrow t=3 \end{gathered}$

We can conclude that it would take 3 hours for the block of ice to melt.