A Graphical Approach

You can draw on the "whiteboard" above. Choose a pen color by clicking on one of the rectangular buttons. Choose a pen width (from fine to coarse) by clicking on a round button. You can clean the whole board by clicking on the gray border. Use the mouse as a pen.

As we are using this whiteboard here, it is a waste of technology. A real (and cheaper) whiteboard, or paper and colored pens, would be much better. But, because this whiteboard is implemented in Java it can be shared by two or more users at distributed locations. As they "talk" in another window or by voice, they can share and both contribute to a single drawing.

We will use the color red for the graph of the height of the water in the right tank. We begin by placing a large red dot at t = 0 high on the graph since the height of the water in the right tank starts out high.

We use the color blue for the graph of the height of the water in the left tank and put a large blue dot at t = 0 low on the graph since the left tank starts empty.

In the beginning the water in the right tank is draining onto the floor and into the left tank. So we draw the red curve decreasing and the blue curve increasing.

Eventually the blue curve hits the red curve (why?) as shown below.

At this point the blue graph is horizontal, since water is neither flowing into or out of the left tank. But the red graph is still going down because water is draining from the right tank onto the floor. Thus, the graphs must cross as shown below. At first the blue graph is decreasing very slowly because the heights of the water in the two tanks are so close. But the red graph continues to drop at a higher rate because the water in the right tank is draining onto the floor. Thus the blue graph must be above the red graph. This answers our question -- there is a time when the water level in the tank on the left is higher than the water level in the tank on the right. It also gives us some idea of why this must be true.

Although this kind of graphic analysis leaves many quantitative questions unanswered, it does give us a very good understanding of why the height of the water in the left tank must be above the height of the water in the right tank at some point in time.