Given that, $ABC$ be a right-angled triangle with $BC$ as the hypotenuse.
Also, $AB=15$ km and $AC=20$ km.
We can draw the diagram.
By using the Pythagorean theorem,
$(BC)^{2} = (AB)^{2} + (AC)^{2}$
$\Rightarrow$ $ (BC)^{2} = (15)^{2} + (20)^{2}$
$\Rightarrow$ $ (BC)^{2} = 225 + 400 $
$\Rightarrow$ $ (BC)^{2} = 625 $
$\Rightarrow$ $ (BC)^{2} = (25)^{2} $
$\Rightarrow$ $ \boxed{BC = 25\;\text{km}} $
The area of the $\triangle ABC,$ we can write in two ways.
$\frac{1}{2}\times AB\times AC = \frac{1}{2}\times BC\times AD$
$\Rightarrow 15\times 20 = 25 \times AD $
$\Rightarrow \boxed{AD = 12\;\text{km}}$
$\therefore$ The required time $= \dfrac{12\;\text{km}}{30 \;\frac{\text{km}}{\text{hour}}} = \dfrac{12 }{30 }\times 60$ minute $= 24$ minutes.
Correct Answer $ : \text{D}$