Answer
$t=\frac{6}{5}$ minutes
Work Step by Step
Step 1: The formula to be used here is $w=\frac{\theta}{t}$.
Step 2: To find $t$, we rearrange the formula to $t=\frac{\theta}{w}$.
Step 3: After substituting the values of $\theta$ and $w$ provided by the question into this formula, the equation becomes $t=\frac{\frac{2\pi}{9}}{\frac{5\pi}{27}}$
Step 4: $t=\frac{2\pi}{9}\times\frac{27}{5\pi}$
Step 5: After simplifying, $t$ is found to be equal to $\frac{6}{5}$ minutes.
