The tortoise and the rabbit were in a 42 kilometer marathon. The rabbit can run 5 times as fast as the tortoise. Less than halfway into the race, the rabbit dropped his lucky rabbit's foot, and so stopped to try and find it. After finding it, he started running to catch up with the tortoise. When the tortoise reached the finishing line, the rabbit was 2 kilometers away. How far (in km) did the tortoise crawl while the rabbit was looking for his lucky rabbit's foot?
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To solve the problem, let's break it down into steps:
Step 1: Determine the speed of the tortoise and the rabbit
Given that the rabbit can run 5 times as fast as the tortoise, let's assume the tortoise's speed is x km/h. Therefore, the rabbit's speed would be 5x km/h.
Step 2: Calculate the time taken by the rabbit to find his lucky rabbit's foot
Since the rabbit stopped to find his lucky rabbit's foot, we don't have information about how long it took. Therefore, we cannot calculate the exact time the rabbit spent searching for the foot.
Step 3: Calculate the distance covered by the tortoise while the rabbit was searching
We know that the race was 42 kilometers, and when the tortoise reached the finishing line, the rabbit was 2 kilometers away. This means that the rabbit still had 2 kilometers left to reach the finishing line. Therefore, the tortoise covered a distance of 42 - 2 = 40 kilometers while the rabbit was searching.
Thus, the tortoise crawled for 40 kilometers while the rabbit was looking for his lucky rabbit's foot.
To find out how far the tortoise crawled while the rabbit was looking for his lucky rabbit's foot, we need to calculate the distance the rabbit covered once he started running again.
Given that the rabbit can run 5 times as fast as the tortoise, we can set up a ratio of their speeds: rabbit's speed / tortoise's speed = 5/1.
Let's assume that when the rabbit stopped to find his lucky rabbit's foot, the tortoise had already covered a distance of x kilometers.
Since the rabbit was 2 kilometers away from the finishing line when the tortoise reached it, we can set up an equation using their respective distances (d) and speeds (s):
Distance covered by the tortoise = x + (42 - x) = 42 kilometers (since it is the total distance of the marathon).
Distance covered by the rabbit = (42 - x) + 2 = 44 - x kilometers.
Now, we can use the ratio of their speeds to set up another equation:
(44 - x) / x = 5/1
Cross-multiplying, we get:
5x = 44 - x
Simplifying the equation, we have:
6x = 44
Dividing both sides by 6, we get:
x = 7.33 kilometers
Therefore, the tortoise crawled approximately 7.33 kilometers while the rabbit was looking for his lucky rabbit's foot.