Changing Spell Lists: how long does it take to change one spell?

Suppose my 10th level wizard wakes up from a good night’s rest and, using all 20 points of his intelligence, he realizes that he needs to change his spell list a little. It’s time to retire Magic Missile, and prepare Fireball instead. The other 14 spells (with a combined spell level total of, say, 35) are not changed.

That is, he is changing one of his 15 prepared spells; the new spell is a 3rd level spell. He is not changing any of his other spells.

My question is, how long does this take? The rules in PHB are a little vague. Page 114 (emphasis mine):

You can change your list of prepared spells when you finish a long rest. Preparing a new list of wizard spells requires time spent studying your spellbook and memorizing the incantations and gestures you must make to cast the spell: at least 1 minute per spell level for each spell on your list.

Is the wizard required to spend the full 38 minutes as if he was preparing an entirely new spell list, or only 3 minutes for the new 3rd level spell?