Question

Andrea and Lauren are $20$ kilometers apart. They bike toward one another with Andrea traveling three times as fast as Lauren, and the distance between them decreasing at a rate of $1$ kilometer per minute. After $5$ minutes, Andrea stops biking because of a flat tire and waits for Lauren. After how many minutes from the time they started to bike does Lauren reach Andrea?

$20$

$30$

$55$

$65$

$80$

Solution:

Let Lauren's rate be $r$ km/min. Then $r + 3r = 1,$ so $r = \dfrac14.$

In the first $5$ minutes the gap shrinks by $5$ km, leaving $15$ km. Lauren covers this alone at $\dfrac14$ km/min, taking $\dfrac{15}{1/4} = 60$ minutes.

The total time is $5 + 60 = 65$ minutes.

Thus, the correct answer is D.

2009 AMC 10A Problem 20

Solution:

Problem 20 in Other Years