Here is a beautiful problem. This problem starts with a minimum of assumptions and soars to great heights in its simplicity of solution using high school calculus. It is called a "marvellous problem" by Carl M Bender and Steven A Orszag on page 33 of their legendary book Advanced Mathematical Methods for Scientists and Engineers. Now be warned. Once you are captured by this problem its beauty could lead you on mathematical travels to distant places. Here is the Snowplow Problem.
One day it started snowing at a heavy and steady rate. A snowplow started out at noon, going 2 miles the first hour and 1 mile the second hour. What time did it start snowing?
11 :23 AM