Two runners (Mr. A and Mr. B) stand exactly 10 miles apart. A fly rests on Mr. A's chest. The two men run straight toward each other (each running at 5 miles per hour), and at the same moment the fly flies off of Mr. A heading straight toward Mr. B at 8 miles per hour. When the fly reaches Mr. B, it immediately turns around and flies back toward Mr. A. The fly continues to reverse directions every time it reaches one of the runners. How far will the fly have traveled when the two runners smash into each other? Assume that all three of them maintain constant speeds.

This puzzle isn't as hard as it may seem at first. The important thing to know is the equation relating time, distance, and speed:
Distance = Rate times Time
If we know the rate and the time, we can easily calculate the distance.

Ignore all of the zigzag movements, and just focus on the total time that the fly is in flight. Each runner is moving at 5 mph. It will take them one hour to meet in the middle of the ten-mile course. If the fly is moving at 8 mph for that hour, it will fly exactly eight miles.