Question

Suppose that w and t vary inversely and that t= 1/5 when w = 4. Write a function that models that inverse variation, and find t when w = 9

Answer 1

Solution

Step 1:

Write an equation that shows that w and t vary inversely

$\text{w = }\frac{k}{t}$

Step 2:

$\begin{gathered} Use\text{ w = 4 and t = }\frac{1}{5}\text{ to find k} \\ 4\text{ = }\frac{k}{\frac{1}{5}} \\ \text{4 = 5k} \\ \text{k = }\frac{4}{5} \end{gathered}$

Step 3

$\begin{gathered} w\text{ = }\frac{4}{5t} \\ 9\text{ = }\frac{4}{5t} \\ 5t\text{ }\times\text{ 9 = 4} \\ 45t\text{ = 4} \\ \text{t = }\frac{4}{45} \end{gathered}$

Final answer

$\begin{gathered} Function\text{ that models that inverse variation is w = }\frac{4}{5t} \\ t\text{ = }\frac{4}{45} \end{gathered}$