Translation:They went with the boat not knowing that a storm was coming.
Another unnatural translation: One can go OUT with a boat, or one can go ON a boat. To go with a boat sounds involuntary, or as if you were accompanying the boat on a transport. It might work in the sense "decided on" but I doubt that was the intended meaning here. Please address these issues in the next revision, as they seriously lower the overall quality of the course.
It's not unusual English in my experience (Irish, native English speaker), though it's less common I suppose. Usually we'd use it to imply that it was their own boat rather than say a public ferry ... "How did your brother get there ?" "Oh he went with the boat/with the car/etc."