2022 AMC 8 Problems/Problem 10
Contents
Problem
One sunny day, Ling decided to take a hike in the mountains. She left her house at , drove at a constant speed of miles per hour, and arrived at the hiking trail at . After hiking for hours, Ling drove home at a constant speed of miles per hour. Which of the following graphs best illustrates the distance between Ling’s car and her house over the course of her trip?
Solution 1 (Analysis)
Note that:
- At Ling's car was miles from her house.
- From to Ling drove to the hiking trail at a constant speed of miles per hour.
It follows that at Ling's car was miles from her house.
- From to Ling did not move her car.
It follows that at Ling's car was still miles from her house.
- From Ling drove home at a constant speed of miles per hour. So, she arrived home hour later.
It follows that at Ling's car was miles from her house.
Therefore, the answer is
~MRENTHUSIASM
Solution 2 (Elimination)
Ling's trip took hours, thus she traveled for miles. Choices , , and are eliminated. Ling drove miles per hour (mph) to the mountains, and mph back to her house, so the rightmost slope must be steeper than the leftmost one. Choice is eliminated. This leaves us with .
Solution 3 (Elimination)
Using the formula, and plugging in the values mph and hrs, we get that the distance from Ling's house to the mountains is miles. That means the first slope ends at so choices and are eliminated.
Furthermore, if the distance is miles, and Ling is returning home at mph, it must have taken her hours. Adding and (how long she hiked for) to her arrival time, AM, we see she must have come back home at PM. Choice is eliminated, so the only valid choice left is choice
~ProProtractor
Video Solution by Math-X (First understand the problem!!!)
https://youtu.be/oUEa7AjMF2A?si=GriQR9m9WenwQVdf&t=1311
~Math-X
Video Solution (CRITICAL THINKING!!!)
~Education, the Study of Everything
Video Solution
https://www.youtube.com/watch?v=Ij9pAy6tQSg&t=733
~Interstigation
Video Solution
https://youtu.be/1xspUFoKDnU?t=332
~STEMbreezy
Video Solution
~savannahsolver
Video Solution
~harungurcan
See Also
2022 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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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