Hare and Tortoise of Aesop's fable fame are having a rematch, a mile-long race. Hare has planned more carefully this time. Five minutes into the race, he figures he can take a \(40-\mathrm{min}\) nap and still win easily because it takes him only \(10 \mathrm{~min}\) to cover \(1 \mathrm{mi}\) and because he thinks that Tortoise's top speed is \(1.0 \mathrm{mi} / \mathrm{h}\). However, Tortoise has been working out, and as he passes napping Hare, he suddenly increases his speed to \(\frac{5}{3} \mathrm{mi} / \mathrm{h}\). When Hare wakes up, he sees Tortoise way ahead and runs at full speed to try to catch up.