A tortoise and a hare start at the same time in a 10-mile race. The hare runs for 20 minutes at 12 mph; stops to rest; falls asleep for several minutes; awakes; and finishes the race, again running at 12 mph. Meanwhile, the tortoise plugs along at the same constant rate of 2 mph throughout the race. What is the least amount of time the hare was asleep if the tortoise wins the race?
(Source: Adapted from Mathematics Teaching in the Middle School, Mar-Apr 1997)