Question

Two hikers are walking along the Appalachian Trail. The first hiker is 2 miles ahead of the second hiker. Both hikers are traveling in the same direction at the same speed, 1 mile per hour. Let x represent the distance traveled by the first hiker after a certain time period.

Several students wrote equations for this situation. Which student is correct?


A.

Alex said, “The equation y = 2x + 1 represents the total distance traveled by both hikers.”



B.

Brenda said, “The equation y = 3x represents the total distance traveled by both hikers.”



C.

Chris said, “The equation y = x – 2 represents the distance traveled by the second hiker.”



D.

Drake said, “The equation y = x + 2 represents the distance traveled by the second hiker.”

Answer 1

C. Chris said, “The equation y = x – 2 represents the distance traveled by the second hiker.”

Explanation:

Answer 2

Chris is correct. (Choice letter C)

Explanation:

We can eliminate choices A and B from the get-go because the problem stated that both hikers are traveling at 1mi/hr. This means that the slope of the equation would equate to 1, so just x.

That leaves us with C and D. The two equations both have a slope of 1, but C has a y-intercept of -2 and D has a y-intercept of 2, which represents the starting location of the second hiker. The first hiker is the one who is ahead by 2 miles, so it can't be D. This leaves us with choice C. Chris is correct.