Question

Comparing Two Functions
Bus Stop: A graph has time (minutes) on the x-axis, and distance (miles) on the y-axis. A line goes through points (0, 5), (6, 8), and (12, 11). Friend's house: A 2-column table with 3 rows. Column 1 is labeled Time (minutes) with entries 3, 6, 9. Column 2 is labeled Distance (miles) with entries 4, 6, 8.

Recall that Seth's house is 17 miles from school. Which location should Seth start off at to get to school faster and how long will it take?


from the bus stop is faster, taking 17 minutes
from the bus stop is faster, taking 24 minutes
from his friend’s house is faster, taking 15 minutes
from his friend’s house is faster, taking 22.5 minutes

Answer 1

For the bus stop the line has slope (8−5)/6 = 0.5, so distance = 5 + 0.5t. Set 5 + 0.5t = 17 → 0.5t = 12 → t = 24 minutes.

For the friend’s house the table gives slope (6−4)/(6−3) = 2/3, and using (3,4) yields distance = (2/3)t + 2. Set (2/3)t + 2 = 17 → (2/3)t = 15 → t = 22.5 minutes (22 min 30 sec).

So starting from his friend’s house is faster, taking 22.5 minutes.