Two cars (A and B) start at the starting line at the same time on a 3-mile long track, going in opposite directions. As they drive around the course, they pass each other many times. Exactly one hour after starting, they pass each other for the 33rd time. At this point car A has completed exactly 20 laps. What is the average speed of Car B?

(In reply to Lapped again (spoiler) by Steve Herman)

Perhaps I wasn't clear on why the fast solution works.  The first time that A and B pass, they have gone a total of one lap, no matter what speed they traveled -- A covers part of the lap in one direction and B covers the rest of the lap in the other direction.  The 2nd time they pass they have covered two laps in total.  The 33rd time they pass they have covered 33 laps in total.  If A has done 20 of those laps in the hour, then B has done 13 laps in the same hour.  Therefore, B has averaged 33 miles per hour.

Posted by Steve Herman on 2014-01-29 16:10:13