Olympiad Maths Prep

Track / Stage 4 / 279 of 340 #539 of 2000

Problem 539

AMC 12 late, AIME early
Algebra Difficulty 4.9 Find the answer

84. Three cars. Three friends are driving in cars along a road in the same direction and at some point in time are positioned relative to each other as follows. Andrews is at some distance behind Brooks, and Carter is at a distance twice that from Andrews to Brooks, ahead of Brooks. Each driver is traveling at a constant speed, and Andrews catches up with Brooks in 7 minutes, and then catches up with Carter 5 minutes later.

How many minutes after Andrews will Brooks catch up with Carter?

Official solution

84. Brooks will catch up to Carter in 6236 \frac{2}{3} min.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.