Skip to main content

2009 AMC 10A Problem 20

Problem 20 of 25HarderAlgebra

Andrea and Lauren are 2020 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 11 kilometer per minute. After 55 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?

Answer choices

Show solution

Solution

Let Lauren’s rate be rr km/min. Then r+3r=1,r + 3r = 1, so r=14.r = \dfrac14. In the first 55 minutes the gap shrinks by 55 km, leaving 1515 km. Lauren covers this alone at 14\dfrac14 km/min, taking 1514=60\dfrac{15}{\frac{1}{4}} = 60 minutes. The total time is 5+60=655 + 60 = 65 minutes. Thus, the correct answer is D.

More practice

Concepts: distance rate and time · rate

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.