Final answer:
The distance of closest approach is 10 km and it takes 0.5 hours for the ships to reach it.
Step-by-step explanation:
The distance of closest approach can be found using the concept of relative velocity. Ship A is steaming west at 20 km/hr and ship B is steaming north at 20 km/hr. We can break down their velocities into horizontal and vertical components. Ship A has a horizontal velocity of -20 km/hr (westward) and ship B has a vertical velocity of 20 km/hr (northward).
To find the distance of closest approach, we need to find the time it takes for the horizontal distance between the two ships to become zero. Since the horizontal components of their velocities are opposite in direction, the distance of closest approach will be the sum of their initial horizontal distances.
The initial horizontal distance between the ships is 10 km. The time it takes for this distance to become zero can be found using the equation distance = velocity x time. Thus, 10 km = (-20 km/hr + 20 km/hr) * time. Solving for time, we get time = 0.5 hours.
Therefore, the correct answer is (a) 10 km, 0.5 hours.