How long would it take for a luxury liner like the Titanic to cross the Atlantic?

The Titanic was supposed to beat the five day crossing time that was the quickest time for passenger ships of its day.

Columbus did not know about the Gulf Stream and a few other navigational tricks. His ships used sails. The first crossing reportedly took five weeks to get to land fall. That was from the Canary Islands and not England. His land fall also was short of the continent. 

The top speed of Columbus's ships was about 8 knots, more realistic 4 knots.

The Titanic was designed to do 24 knots, day in, day out, 24/7.

Gosh - the things you could learn if you only had internet access.