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?

The red line is the finish line at 10 miles. We can see that the tortoise will finish in five hours.

At this point, time is ticking away, but the hare is napping so all that needed to be done was to play around with the minimum amount of time he could nap if he is to lose. Using GSP, I changed the origin to be a floating y-value and x to be stationary at four miles.

Another way to say this is the minimum amount of time the hare can sleep and lose the race is 4 hours 10 minutes and 49 seconds.

Click here to see a GSP file.