That's a good suggestion. Can you think of any game/story situations where "first to the finish line" would matter?
A small child is missing, and the player find out that the Bad Guy is using her to cast an ascension ritual ... but where? The player is given a lock of hair by her distraught parents, and the race is on...
or
As a variation, the player finds out that the Bad Guy
wants the small child for an ascension ritual. He rushes over to protect her, but arrives at the same time as the Bad Guy. They fight, stalemate occurs, much verbosity which indicates that he hasn't got her yet but with the Awesome Power at his fingertips it's only a matter of time, then he runs off to start his ritual, taking the girl's teddy bear with him. The player grabs a link, too, and the race is on...
or
The players break into the Bad Guy's (formerly) secret lair in the hopes of interrupting the Death Ritual he's casting against one of the players. Unfortunately, he is nearling completion, and is safely inside a high-strength ward which must be broken down with powerful magic ... and soon. The race is on.