Question

One sunny day, Ling decided to take a hike in the mountains. She left her house at $8$ a.m., drove at a constant speed of $45$ miles per hour, and arrived at the hiking trail at $10$ a.m. After hiking for $3$ hours, Ling drove home at a constant speed of $60$ 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:

She drives $45$ miles per hour for $2$ hours, so the trail is $90$ miles from her house. The graph must rise from $0$ to $90$ miles between $8$ AM and $10$ AM, then stay flat for the $3$ -hour hike.

She starts home at $1$ PM. Driving $90$ miles at $60$ miles per hour takes $1.5$ hours, so she gets home at $2{:}30$ PM. This matches choice E.

Thus, the correct answer is E.

2022 AMC 8 Problem 10

Solution:

Problem 10 in Other Years