You have a tank that is one (1) mile cubed. How long does it take to drain the tank if they hole that is at the bottom allows a flow rate (initially) of one (1) gallon a second?
You can assume it is totally filled and has water (although it is not important what it is).
Let E be an extension field of F, and let a, B be contained in E. Suppose a is transcendental over F but algebraic over F(B). Show that B is algebraic over F(a).