Two ferry boats serve the same route on a river, but travel at different speeds. They depart from opposite ends of the river at the same time, meeting at a point 720 yards from the nearest shore.
When each boat reaches the other side, it takes 10 minutes to unload and load passengers, then begins the return trip. This time, the boats meet at a point 400 yards from the other shore.
How wide is the river?
The ferry boat problem is created by well-known puzzle author Sam Loyd.
At the first meeting point, the total distance traveled by both boats is the width of the river. When the boats meet again, they’ve each traveled the full width of the river individually, plus another width of the river combined – so they’ve traveled 3 widths of the river combined at that point, thus each traveling 3 times as far as when they first met.
So at this second meeting point, one boat has traveled 3 x 720 yards, leaving it 400 yards away from shore. So the width of the river is the distance traveled by that boat at the second meeting point minus the extra distance it is from the shore: 3 x 720 – 400 = 1,760.
Alternatively, you can set up a proper system of 4 equations that gives you the same result. You may notice that the 10 min loading time is a complete red herring, it does not factor into the calculation at all.