One of the nastiest examples of this type of problem involves two locomotives, heading toward each other at 10 mph. When they are exactly 30 miles apart, a bird sitting on the front of one locomotive flies off toward the other, traveling at 60 mph. When it reaches the other locomotive, it immediately turns around and flies back to the first. The bird continues like this until, sadly, it is smashed between the two locomotives as they collide. When asked how far the bird traveled, many calculus students will spend hours trying to set up and sum impossibly difficult infinite series. Most younger students who have never heard of an infinite series will instead determine that it took the locomotives 1.5 hours to close the 30 mile gap, and that in that time a bird traveling 60 mph would have traveled 90 miles.