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?
Or, if you don't like the last solution, we can calculate as if they are both going a constant speed.
Car A goes 20 laps (60 miles) in 60 minutes, so he goes 1 mile per minute.
They meet 33 times in 60 minutes, so they meet every 60/33 = 20/11 minutes.
In that time, A has gone 20/11 miles.
So B has gone 3 - 20/11 = 13/11 miles.
B's speed is therefore (13/11 miles)/(20/11 minutes) = 13/20 miles/minute = 39 miles per hour