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Problem 508

AMC 12 late, AIME early

Combinatorics Difficulty 4.9 Find the answer

In the race between the tortoise and the hare, the hare initially ran quickly, taking the lead over the slowly crawling tortoise. When the hare believed it could win, it stopped for a nap. Meanwhile, the tortoise maintained a steady pace throughout the race. When the hare woke up and ran towards the finish line, it found that the tortoise had already arrived. The graph that can describe the relationship between distance and time during the race is ( ).

This was a multiple-choice question, but the options didn't survive into the source we have, so there is nothing here to pick from. Work it on paper and mark yourself against the solution below.

Official solution

5. B.

Since the turtle crawls at a constant speed, option D is not correct.

When the rabbit rests, its speed is 0, so the distance during this period is constant. Therefore, options C and E are not correct.

Since the turtle eventually wins, option A is not correct, and option B is correct.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.