$t$ is inversely proportional to $w$. $t=9$ when $w=8$ a) Use the information above to write an equation for $t$ in terms of $w$. b) What is the value of $t$ when $w=5$ ? Give any decimal answers to 1 d.p.

Step 1 ：Given that $t$ is inversely proportional to $w$, we can write the equation as $t = \frac{k}{w}$, where $k$ is a constant of proportionality.

Step 2 ：We are given that $t=9$ when $w=8$. We can use this information to find the value of $k$.

Step 3 ：\(9 = \frac{k}{8}\)

Step 4 ：\(k = 9 \times 8 = 72\)

Step 5 ：Now that we have the value of $k$, we can write the equation for $t$ in terms of $w$ as $t = \frac{72}{w}$.

Step 6 ：Next, we need to find the value of $t$ when $w=5$.

Step 7 ：\(t = \frac{72}{5} = 14.4\)

Step 8 ：\(\boxed{\text{a) The equation for } t \text{ in terms of } w \text{ is } t = \frac{72}{w} \text{.}}\)

Step 9 ：\(\boxed{\text{b) The value of } t \text{ when } w=5 \text{ is } 14.4\)}