Tuesday, June 2, 2020

06/02/2020 (2019: AMC 8, Problem 5)

Q: A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance d traveled by the two animals over time t from start to finish?

2019 AMC 8 -4 Image 1.png

2019 AMC 8 -4 Image 2.png
We know that the tortoise is traveling at a steady rate and that it reaches the end before the hare, making the straight line end (horizontally) before the 'crooked' line does. That means the answer is B, C, or E.
We know that the hare stops, so there must be a horizontal part to the 'crooked' line because the distance remains the same for a length of time. The only graph out of B, C, or E to have a horizontal part is B, so the answer is B.

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