Two soldiers, William and Ethan, are assigned to guard a bridge, which connects the West and East sides of the Great Kingdom. Each soldier is ordered to stand at an end of the bridge to make sure no criminals cross.
On one side of the bridge stands William, watching over the West side of the kingdom, and making sure no shady characters try to cross the bridge.
Ethan stands on the other side of the bridge, facing the East side of the kingdom with his rifle at the ready in case any criminals try to pass across.
"Any criminals today?" William asks.
Ethan rolls his eyes. "What do you think?" he asks.
"You roll your eyes too much," William says.
How could William tell that Ethan was rolling his eyes?
William is on the east side of the bridge, facing the West side of the kingdom, while Ethan is on the west side of the bridge, facing the East side of the kingdom. So William and Ethan are facing each other, and can see each other's faces.
Two trains are traveling toward each other on the same track, each at 60 miles per hour. When they are exactly 120 miles apart, a fly takes off from the front of one of the trains, flying toward the other train at a constant rate of 100 miles per hour. When the fly reaches the other train, it instantly changes directions and starts flying toward the other train, still at 100 miles per hour. It keeps doing this back and forth until the trains finally collide.
If you add up all the distances back and forth that the fly has travelled, how much total distance has the fly travelled when the trains finally collide?
The fly has travelled exactly 100 miles. We can figure this out using some simple math. Becuase the trains are 120 miles apart when the fly takes off, and are travelling at 60 mph each, they will collide in exactly 1 hour. This gives the fly exactly 1 hour of flying time, going at a speed of 100 miles per hour. Thus, the fly will travel 100 miles in this hour.