Two young mathematicians discuss the chain rule.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Riley! Something is bothering me.
Riley
What is it?
Devyn
It’s about rates of change.
Riley
That’s just a derivative. What’s the issue?
Devyn
It might take a bit of setup. Suppose my car has a 10 gallon tank. The distance (call it ) I can drive, without filling up, is miles, where is my car’s fuel efficiency, in miles per gallon.
Riley
Sure. So if you’re getting miles per gallon, that is miles, so you can drive 350 miles before running out of gas.
Devyn
Right! Now, the fuel efficiency depends on how fast I’m driving. If I’m driving 55 miles per hour, I can get 40 miles per gallon, but if I’m driving 70 miles per hour on the interstate, I only get 30 miles per gallon.
Riley
Oh! So your distance function depends on , but depends on your velocity . That means is really a function of .
Devyn
Exactly! Finding the derivative is easy, but how do I find ?
Riley
Hmmm...
What is ?
Suppose that the fuel efficiency is a linear between mph to mph. What is ?