Cleopatra the Demented
Two bicyclists, Anthony and Beatrice, start 10km apart.
Anthony cycles at 4 m/s towards Beatrice, who cycles at 6 m/s towards him.
Cleopatra the Fly starts on the handlebars of Anthony's bike, and flies at 12 m/s towards Beatrice's.
When she gets there she instantaneously reverses direction and flies back to Anthony's, and then repeats the whole process over and over again.
Eventually the two bikes meet. How far has Cleopatra flown?
When you've worked it out, check out the short answer.