College Algebra & Trigonometry, 2018a

4.9. OPTIMIZATION 251
Exercises 4.9(c)
1) A runner starts running north from a given point running at 5 meters per
second. At the same time, a second runner heads east from the same starting
point, running at 8 meters per second. Represent the distance between the runners
as a function of t, the elapsed time. How long will it take for the runners to
be 150 meters apart?
2) A runner starts running north from a given point running at 10 meters per
second. At the same time, a second runner heads east from the same starting
point, running at 7 meters per second. Represent the distance between the runners
as a function of t, the elapsed time. How long will it take for the runners to
be 200 meters apart?
3) At 1 pm a bicycle is 9 miles due north of an ice cream shop and is traveling
south (towards the ice cream shop) at 15 mph. At the same time, another bike
rider is 2 miles east of the ice cream shop and is traveling east (away from the
ice cream shop) at 12 mph. Represent the distance between the bike riders at
any given time after 1pm. At what time is the distance between the riders at a
minimum? How far apart are they at this point?
4) A car leaves a four-way intersection at 9:15 am, traveling south at 70 mph.
At the same time, another car is 65 miles west of the intersection traveling east
at 55 mph. Express the distance between the two cars as a function of the time
since they left the intersection. At what time are the cars closest together? How
far apart from each other are they at this time?