Difference between revisions of "2019 AMC 8 Problems/Problem 5"

(Solution 1 (Using the answer choices))
(Solution 2)
 
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==Solution 1 (Using the answer choices)==
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==Solution 1==
 
First, the tortoise walks at a constant rate, ruling out <math>(D)</math>
 
First, the tortoise walks at a constant rate, ruling out <math>(D)</math>
 
Second, when the hare is resting, the distance will stay the same, ruling out <math>(E)</math> and <math>(C)</math>.
 
Second, when the hare is resting, the distance will stay the same, ruling out <math>(E)</math> and <math>(C)</math>.
Third, the tortoise wins the race, ruling out <math>(A)</math>.
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Third, the tortoise wins the race, meaning that the non-constant one should go off the graph last, ruling out <math>(A)</math>.
Therefore, the answer is the only one left, <math>(B)</math>
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Therefore, the answer <math>\boxed{\textbf{(B)}}</math> is the only one left.
-Lcz
 
  
==See Also==
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<math>\phantom{Note to the original author of this solution: "we shouldn't be able to edit" is incorrect (if its definition is what I think it is), because I was able to edit. Also, I deleted that, (but did nothing else) }</math>
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==Solution 2==
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First, we know that the rabbit beats the tortoise in the first half of the race. So he is going to be ahead of the tortoise. We also know, while he rested, he didn't move. The only graph portraying that is going to be <math>\boxed{\textbf{(B)}}</math>. This is our answer. ~bobthefam
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Video Solution (Also includes problems 1-10)= https://www.youtube.com/watch?v=5i69xiEF-pk&t=2s
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==also see==
 
{{AMC8 box|year=2019|num-b=4|num-a=6}}
 
{{AMC8 box|year=2019|num-b=4|num-a=6}}
  
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 06:56, 15 August 2020

Problem 5

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

Solution 1

First, the tortoise walks at a constant rate, ruling out $(D)$ Second, when the hare is resting, the distance will stay the same, ruling out $(E)$ and $(C)$. Third, the tortoise wins the race, meaning that the non-constant one should go off the graph last, ruling out $(A)$. Therefore, the answer $\boxed{\textbf{(B)}}$ is the only one left.

$\phantom{Note to the original author of this solution: "we shouldn't be able to edit" is incorrect (if its definition is what I think it is), because I was able to edit. Also, I deleted that, (but did nothing else) }$

Solution 2

First, we know that the rabbit beats the tortoise in the first half of the race. So he is going to be ahead of the tortoise. We also know, while he rested, he didn't move. The only graph portraying that is going to be $\boxed{\textbf{(B)}}$. This is our answer. ~bobthefam

Video Solution (Also includes problems 1-10)= https://www.youtube.com/watch?v=5i69xiEF-pk&t=2s

also see

2019 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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