A harbour lies in the direction 60 ^ o south-west from a fort and...

Let $A$ be the position of the harbour and $O$ be of the fort. $OA = 30, OB = 70$. Let $AB = x$.

Applying cosine formula in $\delta OAB$, we get

$cos{60}^{o} = \dfrac{O{A}^{2} + A{B}^{2} - O{B}^{2}}{2OA . AB}$

$⇒ \dfrac{1}{2} = \dfrac{900 + {x}^{2} - 4900}{2 \times 30 \times x}$

$⇒ {x}^{2} - 30x - 4000 = 0$

$⇒ x = 80$

$AB = 80$ kms

Speed of ship =$10$ km/hr

$∴$ Time =$8$ hrs