¶ 2022 AMC8 Problem 10
Problem:
One sunny day, Ling decided to take a hike in the mountains. She left her house at a.m., drove at a constant speed of miles per hour, and arrived at the hiking trail at a.m. 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?
Answer Choices:
A. 
B. 
C. 
D. 
E. 
Solution:
It took Ling hours to drive from her house to the hiking trail, driving at a speed of miles per hour. This means the trail was miles from her house. She arrived at and hiked for hours, so she left the trail at . She then drove home, covering a distance of miles at a speed of miles per hour. Hence the return trip took hours, and Ling arrived at home at PM.
Graphs and are the only ones where Ling drove miles to reach the trail. Graphs and are the only ones where she returns home at . This means the correct answer must be .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions