The following problem is from The Nine Chapters of the Mathematical Art and determines a homogeneous linear system of five equations in six unknowns. Show that the system has infinitely many solutions, and find the one for which the depth of the well and the lengths of the five ropes are the smallest possible positive integers. Suppose that five families share a well. Suppose further that 2 of As ropes are short of the wells depth by one of Bs ropes. 3 of Bs ropes are short of the wells depth by one of Cs ropes. 4 of Cs ropes are short of the wells depth by one of Ds ropes. 5 of Ds ropes are short of the wells depth by one of Es ropes. 6 of Es ropes are short of the wells depth by one of As ropes.

L21 - 2 To solve a related rates problem: 1. Identify the desired rate of change; assign variables to all related quantities. Determine what rate(s) are given at a particular instant in time and express using your variables. Draw a...