2022 AMC 8
Complete problem set with solutions and individual problem pages
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?
- A.
- B.
- C.
- D.
- E.
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
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 .
