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
.
Video Solution
https://www.youtube.com/watch?v=Ij9pAy6tQSg&t=733 ~Interstigation
Video Solution
https://youtu.be/1xspUFoKDnU?t=332
~STEMbreezy
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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