Two hikers are walking along the Appalachian Trail. The first hiker is 2 miles ahead of the second hiker. Both hikers are travel
ing 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.”
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.
