Hello, Fnus!

It took me a few tries to get the first one . . .

I assume that "30°T" is the usual bearing. Code:

| 6t A
C * - - - - *
| *: *
| * : *
| * : *
6√3t | 12t* : *
| * : *
|30°* :6√3t *
| * : *
| * : *
|* : *
* - - - - * - - - - - - - - - * - - - - - - *
P D B Q
: - 6t - : - - 100-14t - - - : - - 8t - - :

In hours, ship **A** sails at 12 kph from to : .

Since is a 30-60 right triangle, we have;

. .

Ship **B** starts from point

In hours, it sails km to

Hence: . and

The distance between the ships is

From right triangle , we have: .

Hence: .

Therefore: . . **(a)**

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Let

Differentiate and equate to zero: .

. . hours

The distance is a minimum in hours ≈ 4 hours, 36 minutes.

Therefore, the ships are closest at .**(c)**

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The desired minimum value is:

. .**(b)**