You and a friend are running laps around a race track. You begin together, and both of you run at constant speed, but you run faster than she does. Because the time interval \(T_{y}\) you take to complete one lap is smaller than the time interval \(T_{f}\) your friend takes to complete one lap, you finish the first lap ahead of her. Each lap you get farther ahead, until eventually you overtake your friend after she has run \(n\) laps (Figure 17.29). What is the frequency \(f_{\text {overtake }}\) at which you overtake her? Express your answer in two ways: first in terms of \(T_{y}\) and \(T_{\mathrm{f}}\) and then in terms of the frequencies \(f_{y}\) and \(f_{f}\) at which each of you completes one lap.

Data from Figure 17.29

Transcribed Image Text:

Figure 17.29 Example 17.6. On each lap, you pull farther ahead... Olap counter 2 you- friend 2 500 track ...eventually, you "lap" your friend (complete one more lap).