In a relay race, Ainslee runs the first lap in 72 seconds. Bridget runs the next lap at $\frac{9}{10}$ of Ainslee's speed. Cecilia runs the next lap at $\frac{4}{3}$ of Bridget's speed. Dana runs the last lap at $\frac{6}{5}$ of Cecilia's speed. What is their total time, to the nearest second?

(A) 4 minutes, 48 seconds

(B) 4 minutes, 22 seconds

(C) 5 minutes, 27 seconds

(D) 4 minutes, 37 seconds

(E) 3 minutes, 46 seconds
Since Bridget runs the second lap at $\frac{9}{10}$ of Ainslee's speed, then it takes her $\frac{10}{9}$ as long to run the lap, or $\frac{10}{9}(72)=10(8)=80$ seconds.

(If the lap length is $d$ and Ainslee's speed is $v$, then the amount of time that Ainslee takes is $t=\frac{d}{v}$ and so the amount of time that Bridget takes is $\frac{d}{\frac{9}{10} v}=\frac{10}{9} \frac{d}{v}=\frac{10}{9} t$.)

Similarly, Cecilia's time for the third lap is $\frac{3}{4}(80)=3(20)=60$ seconds and Dana's time for the fourth lap is $\frac{5}{6}(60)=5(10)=50$ seconds.

Therefore, the total time is $72+80+60+50$ seconds or 262 seconds or 4 minutes, 22 seconds.

ANSWER: (B)