Roxy and Yuri like food

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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?

1 : 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.

1.1 : You might want to try drawing a graph of this situation.

yes no There is no way to tell.

2 : 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.

2.1 : You might want to try drawing a graph of this situation.

yes no There is no way to tell.

3 : 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.