The correct answer is B. 4 hours.
The inlet time is the time it takes for water to flow from the critical point to the mouth of the drain. It can be calculated using the following equation:
$$t = \frac{L}{v}$$
where $t$ is the inlet time, $L$ is the length of overland flow, and $v$ is the velocity of overland flow.
The velocity of overland flow can be calculated using the following equation:
$$v = \sqrt{\frac{g}{S}}$$
where $g$ is the acceleration due to gravity and $S$ is the slope of the overland flow.
In this case, $L = 13.58 \text{ km}$ and $S = 0.001 \text{ m/m}$. Therefore, the velocity of overland flow is:
$$v = \sqrt{\frac{9.8 \text{ m/s}^2}{0.001 \text{ m/m}}} = 31.3 \text{ m/s}$$
The inlet time is then:
$$t = \frac{13.58 \text{ km}}{31.3 \text{ m/s}} = 4.3 \text{ hours}$$
Since the inlet time is rounded to the nearest hour, the correct answer is B. 4 hours.
Option A is incorrect because it is the time it takes for water to flow from the critical point to the drain mouth if the velocity of overland flow is 20 m/s. However, the velocity of overland flow in this case is 31.3 m/s, so the inlet time is shorter than 2 hours.
Option C is incorrect because it is the time it takes for water to flow from the critical point to the drain mouth if the velocity of overland flow is 40 m/s. However, the velocity of overland flow in this case is 31.3 m/s, so the inlet time is shorter than 4 hours.
Option D is incorrect because it is the time it takes for water to flow from the critical point to the drain mouth if the velocity of overland flow is 60 m/s. However, the velocity of overland flow in this case is 31.3 m/s, so the inlet time is shorter than 8 hours.