The Tortoise and the Hare

The big idea

The twist: The hare was faster at every moment he was running. He still lost.

The big idea: What wins a race is average speed. Total distance divided by total time, and time spent resting counts. If the hare ran 10 times faster but rested for 95% of the race, his average speed dropped below the tortoise's.

Biology adds another layer. Hares are built for short sprints to escape predators, using muscles that tire quickly. Tortoises are built for slow, steady energy use. Each animal is good at a different kind of race.

Average speed: the hare’s real problem

Average speed = total distance ÷ total time.

The important word is total. Time spent stopped still counts, because the clock keeps running while the hare naps. Here’s an example race with made-up numbers:

• The race: 100 metres.
• The hare sprints at 10 metres a second. He reaches 90 metres in 9 seconds, then naps for 1 hour (3,600 seconds), wakes and finishes the last 10 metres in 1 second. His total time is 3,610 seconds, so his average speed is 100 ÷ 3,610 ≈ 0.03 metres a second.
• The tortoise plods at 0.05 metres a second and never stops. He finishes in 2,000 seconds, about 33 minutes. His average speed is 0.05 metres a second.

The hare’s top speed was 200 times the tortoise’s, but his average was lower. Being fast only helps when you’re moving. Stops don’t just pause your progress; they drag your average down.

A trap worth knowing: average speed isn’t the average of your speeds. Suppose you cycle to Grandma’s at 20 km/h and come back at 10 km/h. It’s tempting to say you averaged 15 km/h, but the slow trip home takes twice as long, so you spend more time going slowly. If Grandma lives 20 km away, the trip there takes 1 hour and the trip back takes 2 hours. That’s 40 km in 3 hours, an average of about 13.3 km/h.

Marathons: where steady really wins

A marathon is 42.195 km. The odd distance comes from the 1908 London Olympics, where the course was set so the race could start at Windsor Castle and finish in front of the royal box. That length later became the official standard.

Even pacing beats fast-then-slow. Your muscles mainly run on a stored fuel called glycogen, and there’s only enough for a limited distance. Start too fast and you burn through it early. Many runners “hit the wall” somewhere around 30 km: their legs suddenly feel heavy and they slow down dramatically. That’s the hare’s mistake in real life.

The best marathon runners do the opposite. They aim for a steady pace, or even a slightly faster second half, which runners call a negative split. Many record-breaking runs have been paced very evenly from start to finish.

How fast is “steady” at the top level? In 2019, Eliud Kipchoge ran a marathon in 1 hour 59 minutes 40 seconds. It was a special event, not an official record. His average speed was about 21 km/h, which is roughly:

• 1 km every 2 minutes 50 seconds
• 100 metres every 17 seconds, kept up for nearly two hours

Most children can sprint 100 metres faster than 17 seconds, but only for a few seconds. Kipchoge’s skill was keeping a quick pace without ever stopping or slowing. He’s a tortoise with the speed of a hare. Pacemakers ran in formation around him, and a car ahead projected laser lines on the road to show the target pace. It was all about steadiness.

Let’s try together

• Walk test: time a walk round the block. Then walk it again, stopping for 30 seconds halfway. Work out the average speed both times. How much did a short stop cost?
• Pacing experiment: run one lap of a park as fast as you can, then a second lap straight away. Next time, run both laps at a steady speed. Which way gives the faster total time?

Question

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