Suppose that you are on a private boat, cruising on a river like you always do. You start at a dock, then steer the boat 1 hour upriver. You then steer the boat back downriver, and go back to the dock. You hear from somebody that your boat's only lifesaver accidentally dropped at the start of your cruise, and has been floating downriver. This causes you to keep on going downriver until you finally catch up to the lifesaver 1 mile downriver from the dock.
The question is: how fast was the river moving?
You may work this out the typical way: setting a variable to be the speed of the boat, setting a variable to be the speed of the river, then solving for it. But there is an easier way.
What is we looked at the point of view of the lifesaver instead o the boat? Relative to the lifesaver, the river is not moving. The boat cruises away for a while, the cruises back to get it. Remember that the river isn't moving, so the boat takes the same amount of time to cruise back to the lifesaver as cruising away. Since it took 1 hour to cruise away, then it takes 1 hour to cruise back, which means that the whole ordeal took 2 hours. The lifesaver floated downriver 1 mile in these two hours, implying the river flows at 0.5 miles per hour.