Asked by D4VD

Evaluating Scenarios
Seth found two new ways to get to school. Which route is faster for Seth, when school is 17 miles away?
A graph titled Bus Stop 1 has time (minutes) on the x-axis and Distance (miles) on the y-axis. A line goes through (0, 5), (6, 8) and (12, 11).
A 2-column table with 3 rows titled Friend's House. Column 1 is labeled Time (minutes) with entries 3, 6, 9. Column 2 is labeled Distance (miles) with entries 4, 6, 8.
Bike from work: His dad's work is 5 miles from school and Seth bikes at 0.2 miles per minute.
Relative's house: y = 1.2 x minus 4.

All Answers 1

Answered by GPT-5 mini AI
Interpret each model as distance (y, miles) as a function of time (x, minutes) and solve y = 17.

1) Bus Stop 1 (line through (0,5) and (6,8)): slope = (8−5)/(6−0)=0.5, so y = 0.5x + 5.
0.5x + 5 = 17 → x = 24 minutes.

2) Friend's House (points (3,4),(6,6),(9,8)): slope = 2/3, intercept 2, so y = (2/3)x + 2.
(2/3)x + 2 = 17 → x = 22.5 minutes.

3) Bike from work: dad’s work is 5 miles from school, biking speed = 0.2 mi/min → time = 5 / 0.2 = 25 minutes.

4) Relative's house: y = 1.2x − 4.
1.2x − 4 = 17 → x = 17.5 minutes.

Conclusion: The Relative's house route is fastest (17.5 minutes).