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A speedy tortoise can run with a speed of 10 cm/s and a hare can run 20 times as fast. They both start at the same time but the hare stops to rest for 2 minutes. The tortoise wins by a shell (20 cm). The race is considered over when the tortoise crosses the finish line.

User Sangmin
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1 Answer

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Let's assume that the race track is a straight line and that the tortoise and hare start at the same point. Since the tortoise wins by a shell (20 cm), we can assume that the tortoise travels a total distance of 100 cm (since 20 cm is 1/5 of the total distance, and the tortoise wins by a small fraction).

Let's first calculate how long it will take the tortoise to run the entire distance:

time = distance / speed = 100 cm / 10 cm/s = 10 s

So the tortoise takes 10 seconds to complete the race.

Now let's calculate how far the hare can run in 2 minutes:

distance = speed × time = 20 × 10 cm/min × 2 min = 400 cm

This means that while the hare rests for 2 minutes, it can run 400 cm before the tortoise reaches the finish line. However, since the hare starts 20 times farther ahead than the tortoise, it has already covered 2000 cm by the time the tortoise reaches the finish line (since the tortoise wins by a shell of 20 cm).

Now let's calculate how long it takes the hare to cover the remaining distance:

time = distance / speed = (2000 cm - 400 cm) / (20 × 10 cm/s) = 8 s

So the hare takes 8 seconds to cover the remaining distance after resting for 2 minutes. However, the tortoise has already crossed the finish line by the time the hare completes the race.

Therefore, the tortoise wins the race.

User Armentage
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