Question

Kelsie is riding her bike towards Anna from 172 feet away, with a speed of 10 feet per second. The distance d of Kelsie from Anna at any time t is modeled by d=∣172–10t∣.

(a) At what time is Kelsie 15 feet away from Anna?
(b) Why is an absolute value equation a useful method to model this situation?

Answer 1

To find the time at which Kelsie is 15 feet away from Anna, we need to solve the equation d = |172 - 10t| = 15. An absolute value equation is a useful method to model this situation because it allows us to consider both the cases when the expression inside the absolute value is positive and negative.

Step-by-step explanation:

(a) To find the time at which Kelsie is 15 feet away from Anna, we need to solve the equation d = |172 - 10t| = 15. We can break the absolute value into two cases: 172 - 10t = 15 and 10t - 172 = 15. Solving the first case gives t = 15.7 seconds, and solving the second case gives t = 15.7 seconds as well. So, Kelsie is 15 feet away from Anna at time t = 15.7 seconds.

(b) An absolute value equation is a useful method to model this situation because it allows us to consider both the cases when the expression inside the absolute value is positive and negative. In this case, the absolute value equation accounts for the fact that Kelsie can either be ahead of Anna or behind Anna, depending on the value of t.