Two ships are 10 km apart on a line running south to north. The one farther north is streaming west at 40 km/hr. The other is steaming north at 40 km/hr. The distance of closest approach and how long do they take to reach it are is

(a) 7.071 km, 1/2 hr
(b) 7.071 km, 1/8 hr
(c) 6 km, 1/8 hr
(d) none of these

Let the first ship steaming north be named A and the other B. The relative velocity of A with respect to B is 40√2 south west.  If we extend the line along the 45° south west from the initial position of A, the distance of closest approach is the perpendicular drawn from B to this line.
So, the distance of closest appraoch = 10 sin 45° = 10/√2 = 7.07 m