A special drill is used at a construction site to dig holes. A hole is dug to a depth of 2.75 feet when the drill hits rock. The progress slows to 56 feet per hour of digging. The depth of the hole must be at least 1012 feet by the end of the day to stay on schedule.

What is the minimum amount of time the drill must continue at its present rate to complete the hole on schedule?

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