How long could the hare sleep and still win the race against the tortoise?

inspired by Aesop’s fable “The Tortoise and the Hare”

This article is also available in Thai.

The Tortoise and the Hare

In the past months I have been reading bedtime stories to my little daughter. She loves Aesop’s “The Tortoise and the Hare” very much and picks the same book everyday (although she cannot read yet).

The story concerns a Hare who ridicules a slow-moving Tortoise. Tired of the Hare’s boastful behavior, the Tortoise challenges him to a race.

The hare soon leaves the tortoise behind and, confident of winning, takes a nap midway through the race.

When the Hare awakes however, he finds that his competitor, crawling slowly but steadily, has arrived before him.

Reading the same book everyday made me start asking ridiculous question about the story wondering how could the rabbit lose … so I conducted an analysis.

I don’t know what kind of race they were in, but for something long enough to have a nap time, let them do a marathon (42.195 km).

🐢 The tortoise has an average speed of 0.27 km/hr. The fastest tortoise can reach 8 km/hr. For the sake of the race to end within a day, I will bless it with the 8 km speed.

🐰 The hare can run 40–70 km/hr. Good luck tortoise.

This plot shows distance over time. The green line represents the tortoise, moved with constant speed without resting until it reached the finish line. The pink lines are for the hare. The thick line shows the best case scenario that the hare could run with maximum speed. The thin line (with the middle part overlaps with the thick line) shows the worst case scenario that the hare ran with minimum speed. The flat part in the middle represents nap time that the hare did not gain any distance.

The line chart above shows that no matter whether the hare performed at its best or worst, it still could take at least four hours nap, which was more than 80% of the time the tortoise had to run non-stop. In other words, the hare could still easily win the race even though it was sleeping 80% of the time. Therefore, that Aesop hare is really a disappointment of its species.

Reference

1. Marathon Wikipedia
2. Speed of a Rabbit or Hare
3. Tortoise Wikipedia
4. The Tortoise and the hare Wikipedia

Appendix

This is the R script I used to draw the plot.