Answer
a) $\Delta t=0.02s$
b) $\Delta t=0.04s$
Work Step by Step
To make the propeller appear stationary, each light in the 3 blades is limited to only one out of three positions where the other light have possessed.
In other words, the time between flashes of light need to be adjusted to be equal to the time it takes one blade to go to one out of those three positions, which is displaced $1/3$ revolutions from one another. In short, $\Delta\theta\in\{1/3, 2/3, 3/3, ... n/3| n\in N\}$
We have $$\Delta t=\frac{\Delta\theta}{\overline\omega}$$
a) $\Delta t$ min when $\Delta\theta$ min, which is $\Delta\theta=1/3$ rev. We have $\overline\omega=16.7rev/s$. So, $$\Delta t=0.02s$$
b) The next shortest time happens when $\Delta\theta=2/3rev$ $$\Delta t=0.04s$$
