The 100-Yard Race
Annie and Amy race each other for a distance of 100 yards. Annie wins by 10 yards. They decide to try again, but to even things up, Annie begins 10 yards behind the starting line. If they both run at the same speed they did earlier, who will win the race?
How fast were they running earlier?
Annie will win again. In the first race, Annie ran 100 yards in the time it took Amy to run 90. In the second race, Annie will have run 100 yards by the time Amy gets to 90 yards, so they will be alongside each other. At this point, they both have 10 more yards to go, and since Annie is a faster runner, she will cross the finish line first.