There’s an old story about a race between a tortoise and a hare. The hare knew he was much faster than the tortoise. He was so confident of winning that he lay down by the side of the road to take a nap. Meanwhile the tortoise just kept going, slowly and steadily towards the finish line.

The hare overslept. When he finally woke up and sped towards the finish, it was too late to catch up. The moral of the story is “slow and steady wins the race.”

Our hare has heard that story many times, so he came away with a different lesson: “Always set your alarm clock.”

On the morning of a 10 kilometer race the hare and the tortoise were at the starting line. As the starting whistle blew the tortoise set off down the road at top speed. For him that was 1 kilometer per hour. The hare set his alarm clock and went to sleep.

The hare was able to run at 5 kilometers per hour. How much of a nap could he take and still win?

Can you come up with a general solution to this problem that will tell the hare how long a nap he can take for any combination of hare speed, tortoise speed and race length?

After you’ve tried this for yourself check our solution.