Question

John is driving around town. When he reaches the gas station, he notes that he has traveled 12 miles. He reaches home 2 hours later and notes that he has traveled 31 miles.

If d represents the distance and t represents the time, in hours, John has traveled since the gas station, which of the following equations can be used to model this situation?
A. d = 9.5t - 12
B. d = 19 + 12t
C. d = 12t + 43
D. d = 9.5t + 12

Answer 1

The student is looking for an equation to model the distance John travels over time since passing the gas station. The correct equation, given his rate of travel and the distances noted, is d = 9.5t + 12, representing the distance d in relation to time t.

Step-by-step explanation:

The student's question involves creating a linear equation (modeling a situation) based on the distance traveled over time. Since the student begins by noting a distance of 12 miles at the gas station and ends up with a total distance of 31 miles 2 hours later, this implies he has traveled an additional 19 miles over 2 hours. The rate of travel is therefore 19 miles / 2 hours = 9.5 miles/hour. We represent the distance traveled since the gas station with d, and the time since the gas station with t. Thus, the equation that models this situation is d = 9.5t + 12.