Hello, scherz0!

I had difficulty reading some of the data.

I hope I got it right . . .

At the very beginning, the diagram looks like this: Code:

* Q
* |
* |
* |
5 * | 5√2/2
* |
* |
* 45° |
P * - - - - - - - * R
5√2/2

Ship is at ; ship is at

Code:

* Q
* |
* | 4t
* |
5 * * B
* * |
* * | 5√2/2-4t
* * |
P * - - - * - - - * R
5t A 5√2/2-5t

In hours, ship has moved km to point

In the same hours, ship has move km to point

Their distance is given by: .

. . which simplifies to: .

Differentiate and equate to zero: .

Therefore, they are closest at: .