Calculating how long does a hare remain stationary in a race

Question

I'm solving book exercises - there's a classic problem involving a hare and a tortoise. This is what I did, but apparently the final answer is wrong.

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Basically it's a 1000m race, both animals have a constant speed (hare at 8m/s and tortoise at 0.2m/s). The hare runs 800m and then stops to tease the tortoise. Then, at some point in the future, the hare resumes and both animals finish at the same time.

(a) How far is the tortoise from the finish line when the hare resumes the race?

Well, since both animals finish at the same time, I just need to find out how long it takes the hare to finish the remaining 200m and then check how much distance could the tortoise cover in that time.

So

$$\frac{200\text{m}}{8\text{m/s}} = 25\text{s}$$

Meaning that the tortoise could cover barely

$$25\text{s}\cdot0.2\text{m/s} = 5\text{m}$$

This appears to be correct according to the book.

(b) For how long in time was the hare stationary?

The hare runs $800\text{m}$ in $8$ seconds, so the tortoise barely covered $1.6\text{m}$ in that time. Since the hare restarts when the tortoise is $5\text{m}$ away from the finish line, it must have waited until the tortoise covered another $(1000 - 5 - 1.6) = 993.4$ meters, which takes $993.4 / 0.2 = 4967$ seconds.

Well apparently that's wrong. The book says the answer is just "$4.88$" (doesn't even mention the units, but even if that were minutes or hours it doesn't match).

What did I do incorrectly?

Answer 1

It doesn't matter when the hare stopped. If he had stopped right before the finish line you would have the same result. So the question is - how much longer does it take the tortoise to cover the course? The hare has to start again after the tortoise passed him, in your formulation of the problem. Otherwise he will not arrive at the same time.

You are wrong when you say the hare runs 800 m in 8 seconds - he runs 8 m/s so it takes him 100 seconds to run 800 meters. Perhaps that's all the fix you need.

But I would do part 2 differently. Calculate the total time it takes the hare and the tortoise respectively. The difference in time is how long the hare waited. I make it 5000-125 = 4875 seconds, or 4.88 ks. Which is a rather unusual unit.