I have used the sledgehammer to crack this one, but have no idea how to do it elegantly!

A ship A is moving eastwards with a speed of 15 km/h and another ship B, at a given instant 10 km east of A, is moving southwards with a speed of 20 km/h. How long after this instant will the ships be nearest to each other, how far apart will they be then, and in what direction will B be sighted from A?

The relative vector didn't tell me much, so I started plotting what happened after one minute then 10, 30 up to 40 when both ships are aligned north south. After 10 minutes, for example, vector AB is the hypotenuse of a triangle 9.5 km (east) and 3.3 km (south) giving a distance between the ships of 8.194 km.

so after 0 |AB| = 10 km

1 |AB| = 9.76

10 = 8.19

20 = 8.34

40 = 13.3

from this I guessed the min distance would be between 1 and 10 minutes and I could have plotted all distances for each minute. But I don't believe this is the way to do it!

Any better suggestions would be appreciated!