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Two young mathematicians discuss the eating habits of their cats.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Yo Riley, I was watching my two cats Roxy and Yuri eat their dry cat food last night.
Riley
Cats love food! It’s so weird that they swallow the pieces whole!
Devyn
I know! I noticed something else kinda funny though: Both Roxy and Yuri start and finish eating at the same times; and while I gave Roxy a little more food than Yuri, less food was left in Roxy’s bowl when they stopped eating.

I wonder, is there is a point in time when Roxy and Yuri have the exact same amount of dry cat food in their bowls?

Riley
Hmmmmm. Do Roxy and Yuri both start and finish drinking their water at the same times? And does Roxy start with a little more water than Yuri, and finish with less water left than Yuri?
Devyn
Yes!
Riley
Interesting. I wonder, is there is a point in time when Roxy and Yuri have the exact same amount of water in their bowls?
Is there a time when Roxy and Yuri have the same amount of dry cat food in their bowls? Make the following assumptions:
• They start and finish eating at the same times.
• Roxy starts with more food than Yuri, and leaves less food uneaten than Yuri.
You might want to try drawing a graph of this situation.
yes no There is no way to tell.
Is there a time when Roxy and Yuri have the same amount of water in their bowls? Make the following assumptions:
• They start and finish drinking at the same times.
• Roxy starts with more water than Yuri, and leaves less water left in her bowl than Yuri.
You might want to try drawing a graph of this situation.
yes no There is no way to tell.
Within the context of the two problems above, what is the difference between “dry cat food” and “water?”
If we write the amount of dry cat food as a function of time, this function is not continuous. The reason it isn’t continuous is that the dry cat food is a collection of individual kibbles, which are eaten whole.

On the other hand, if we write the amount of water as a function of time, this function is continuous.
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