Question

Janie walks 1 mile to get to a running track. She then runs at a speed of 3.5 miles per hour. Which linear model represents the total distance she ran and walked, d, as a function of t, the time she runs, in hours?

Answer 1

Linear model representing the total distance she ran and walked, d, as a function of time, t, can be expressed as:

d(t) = 1 + 3.5t

Explanation:

To represent the total distance Janie ran and walked as a function of time, we need to consider two components: the distance she walks to the running track and the distance she runs on the track.

Distance walked to the running track: Janie walks 1 mile to reach the track. This distance remains constant regardless of the time she spends running.

Distance run on the track: Janie runs at a speed of 3.5 miles per hour. The distance she runs can be calculated by multiplying her running speed (3.5 miles/hour) by the time she spends running (t hours).

Therefore, the linear model representing the total distance she ran and walked, d, as a function of time, t, can be expressed as:

d(t) = 1 + 3.5t

Here, the constant term '1' represents the distance she walks to the track, and '3.5t' represents the distance she runs on the track, where t is the time she spends running in hours.