"Slow and steady wins the race" is a metaphor and usually not to be taken literally. While considered a good rule of thumb by many people there may also be situations in which it does not apply, in particular when those that are already ahead are given further advantages. For example, in the video game League of Legends gaining an early advantage in gold or XP may allow players to "snowball": to accumulate further advantages over their opponents by using their strong position to deny them access to resources.

However, in the concrete example that you are asking about the contestant going at a constant speed would indeed reach the goal before the other contestant. Under the assumption that the contestant going at a constant speed takes one hour to reach the goal the other contestant would take 30 minutes for the first part of the race and one hour for the second part. It would therefore take the contestant that was sprinting at first a total of 90 minutes to finish the race and they would lose to the contestant that is going at a steady pace.
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