According to family lore, my grandfather checked out the prices on the Titanic but couldn’t afford it. He left on a different ship around the same time as the Titanic and supposedly passed it on the way. He claimed all the lights were blazing and the ship was making a leisurely voyage at the time. I guess it was good that he was dirt poor when he left England, lol.
Would not want to contradict your grandpad, but the usual notion is that the Titanic was trying to set a crossing record, and that this was a major contributor to its destruction. So it doesn't seem all that likely that it was poking along.