Rabbit and Fox Riddle: Maximum Safe Distance for a Rabbit | Solution

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In summary, a rabbit can detect a fox at 60 meters through sight, sound, and smell, and will immediately run to its hole. If the fox can run twice as fast as the rabbit, the maximum distance from its hole that a rabbit can safely venture is 40 meters, assuming the rabbit escapes if they arrive at the hole at the same time. This is because the rabbit would always have to be twice as close to the hole than the fox in order to ensure the fox is always 40 meters away. "Twice as close" is equivalent to "half as far".
  • #1
some_letters
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Homework Statement



Through a combination of sight, sound, and smell a rabbit can detect a fox at 60 meters. When the rabbit detects the fox, it runs immediately straight to its hole. If the fox can run twice as fast as the rabbit, what is the maximum distance from its hole that a rabbit can safely venture? Assume that the rabbit escapes if they arrive at the hole at the same time.

2. The attempt at a solution

2x + 60 = x
x = 60

Apparently this is incorrect
 
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  • #2
Does the question state where the hole is compared to the fox and rabbit. Your result is correct if the rabbit is directly between the fox and the hole. but what if the hole was between the fox and rabbit?
 
  • #3
I think I understand now. It would always have to be twice as close to the hole than the fox. A twenty meter radius would ensure the fox is always 40 meters away from the hole.
 
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  • #4
some_letters said:
I think I understand now. It would always have to be twice as close to the hole then the fox. A twenty meter radius would ensure the fox is always 40 meters away from the hole.
Is "twice as close" the same as "half as far" ?
 
  • #5
I think so. why do you ask?
 

1. What is the Rabbit and Fox Riddle?

The Rabbit and Fox Riddle is a classic problem that involves determining the maximum safe distance a rabbit can travel from its burrow while being pursued by a fox.

2. How does the riddle work?

In the riddle, the rabbit and fox are both given a constant speed, and the rabbit must reach its burrow before the fox catches it. The maximum safe distance is the distance from the burrow that the rabbit can travel before the fox catches up.

3. What is the solution to the riddle?

The solution to the riddle is to use the Pythagorean theorem to calculate the distance the rabbit can travel, given the speeds of the rabbit and fox. The maximum safe distance for the rabbit is equal to the square root of the square of the rabbit's speed minus the square of the fox's speed.

4. Why is the Rabbit and Fox Riddle important?

The riddle is important because it challenges critical thinking and problem-solving skills. It also has real-world applications in fields like mathematics, physics, and biology.

5. Is there a formula for solving the riddle?

Yes, the formula for solving the Rabbit and Fox Riddle is: maximum safe distance = √(rabbit's speed² - fox's speed²).

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