#### Answer

The trawler moved with a speed of $28.75~km/h$

#### Work Step by Step

In $4.0~h$, the fish swim $20.0~km$ to the northwest.
We can find the fish's displacement to the north:
$(20.0~km)~sin~45^{\circ} = 14.14~km$
We can find the fish's displacement to the west:
$(20.0~km)~cos~45^{\circ} = 14.14~km$
To intercept the fish, the trawler needs to move $114.14~km$ to the north and $14.14~km$ to the west. We can find the distance $d$ that the trawler must travel:
$d = \sqrt{(114.14~km)^2+(14.14~km)^2} = 115~km$
We can find the trawler's speed:
$v = \frac{d}{t} = \frac{115~km}{4.0~h} = 28.75~km/h$
The trawler moved with a speed of $28.75~km/h$.